Language like “invasion” and the “replacement” of Americans has increasingly become a regular part of Fox News broadcasts, Rush Limbaugh shows and other prominent conservative media.

Tucker Carlson went on his prime-time Fox News show in April last year and told his viewers not to be fooled. The thousands of Central Americans on their way to the United States were “border jumpers,” not refugees, he said. “Will anyone in power do anything to protect America this time,” he asked, “or will leaders sit passively back as the invasion continues?”

When another group approached the border six months later, Ann Coulter, appearing as a guest on Jeanine Pirro’s Fox News show, offered a dispassionately violent suggestion about what could be done to stem the flow of migrants: “You can shoot invaders.”

A few days after, Rush Limbaugh issued a grim prognosis to his millions of radio listeners: If the immigrants from Central America weren’t stopped, the United States would lose its identity. “The objective is to dilute and eventually eliminate or erase what is known as the distinct or unique American culture,” Mr. Limbaugh said, adding: “This is why people call this an invasion.”

There is a striking degree of overlap between the words of right-wing media personalities and the language used by the Texas man who confessed to killing 22 people at a Walmart in El Paso this month. In a 2,300-word screed posted on the website 8chan, the killer wrote that he was “simply defending my country from cultural and ethnic replacement brought on by an invasion.”

It remains unclear what, or who, ultimately shaped the views of the white, 21-year-old gunman, or whether he was aware of the media commentary. But his post contains numerous references to “invasion” and cultural “replacement” — ideas that, until recently, were relegated to the fringes of the nationalist right.

An extensive New York Times review of popular right-wing media platforms found hundreds of examples of language, ideas and ideologies that overlapped with the mass killer’s written statement — a shared vocabulary of intolerance that stokes fears centered on immigrants of color. The programs, on television and radio, reach an audience of millions.

“ We are so overwhelmed by this — it literally is an invasion of people crossing into Texas. ” — Laura Ingraham on “The O’Reilly Factor,” May 29, 2014 “ We are letting folks invade our home, walk into our home, and we won’t even defend it or protect it. ” — Patrick Buchanan on “Hannity,” June 9, 2014 “ This isn’t reunification. This is a government-sanctioned invasion of our country. ” — Todd Starnes on “Fox & Friends Sunday,” July 6, 2014 “ The invasion of illegal immigrants, and in particular unaccompanied children, at our southern border continues to spiral out of control. ” — Sean Hannity on “Hannity,” July 12, 2014 “ When the federal government is not able or is not willing to protect from an invasion, a state has the right to reach its own agreements, levy its own taxes and do whatever it has to, to secure its border from further invasion. And this is an invasion. Twice as big already than D-Day and twice as many again still coming. ” — Louie Gohmert on “Justice With Judge Jeanine,” July 13, 2014 “ The other top story is the fact that we’ve got this invasion across our southern border of all these illegals. Many are children. ” — Steve Doocy on “Fox & Friends,” July 16, 2014 “ In the Constitution, the founding fathers called it repelling invasion. ” — Allen West on “On the Record With Greta Van Susteren,” Aug. 11, 2015 “ Trump’s great accomplishment is to expose the fact that the establishment of this country is responsible for insecure borders, the masses coming across our borders, invading our country. ” — Patrick Buchanan on “Hannity,” Oct. 21, 2016 “ It’s a mass of humanity right now, just walking across the border, coming across the Rio Grande. This is a peacetime invasion of the United States. ” — Laura Ingraham on “Special Report With Bret Baier,” Nov. 16, 2016 “ These are illegal aliens who have invaded our country. And illegal alien equals criminal. ” — Mary Ann Mendoza on “Fox & Friends,” March 29, 2017 “ They used to call that an invasion. And they used to fight wars over stuff like that. But these days it’s a voter registration drive for the D.N.C. ” — Todd Starnes on “Fox & Friends,” May 9, 2017 “ We’re going to be confronted by even more serious invasion, in terms of those crossing the border with drugs. ” — Jeanine Pirro on “Fox & Friends,” July 28, 2017 “ Will anyone in power do anything to protect America this time, or will our leaders sit passively back while the invasion continues? ” — Tucker Carlson on “Tucker Carlson Tonight,” April 2, 2018 “ What else would you call it? It’s gotta be — it’s an invasion of our country and of our rights. It’s just — it’s despicable. ” — Art Del Cueto on “The Ingraham Angle,” April 9, 2018 “ You use the word ‘invasion,’ people say ‘oh, that’s so mean.’ What else do you call this? ” — Laura Ingraham on “The Ingraham Angle,” April 12, 2018 “ We'll also expose the Americans aiding and abetting a mass invasion of illegal immigrants looking to exploit our laws. ” — Laura Ingraham on “The Ingraham Angle,” April 26, 2018 “ It doesn’t look like people seeking asylum, it looks more like an invasion of our country. And that’s sad. ” — Art Del Cueto on “America’s Newsroom,” May 1, 2018 “ We’re going to abolish ICE? I mean that’s the second line of defense to prevent an invasion of the United States and to kick out people who are criminals and child molesters, MS-13. ” — Patrick Buchanan on “Cavuto Live,” July 7, 2018 “ I don’t think we should sit back and get invaded by foreigners. I don’t. That doesn’t make me a racist, it makes me an American. ” — Tucker Carlson on “Tucker Carlson Tonight,” Aug. 20, 2018 “ When MS-13 invades our country — 10,000 members across 40 states — Nancy Pelosi talks about the spark of divinity. ” — Kayleigh McEnany on “America’s Newsroom,” Aug. 23, 2018 “ The reality is, our southern border is on the verge of an invasion. ” — Herman Cain on “Hannity,” Nov. 15, 2018 “ This is not migrants coming into the country. This is nothing short of an invasion. ” — Art Del Cueto on “America’s Newsroom,” Nov. 16, 2018 “ You have our troops at the border and they are meant there for a deterrence effect, to say, don’t come here, don’t invade, you have to go to the proper channels. ” — Morgan Ortagus on “Hannity,” Nov. 17, 2018 “ I.C.E. are the agents — they’re just police officers — who protect this nation from invading illegal immigrants. ” — Sebastian Gorka on “Justice With Judge Jeanine,” Nov. 17, 2018 “ You can’t shoot Americans. You can shoot invaders. ” — Ann Coulter on “Justice With Judge Jeanine,” Nov. 25, 2018 “ This isn’t going to stop the flow of illegals who are invading our country. ” — Mary Ann Mendoza on “Fox & Friends First,” Feb. 1, 2019 “ There is an invasion going on right now. ” — Jeff Crouere on “America’s News HQ,” March 10, 2019 “ What about us? What about our country? We’re being invaded. ” — Tucker Carlson on “Tucker Carlson Tonight,” April 9, 2019 “ We are going to change the underlying broken laws to stop what I think is literally an invasion of people from Central America. ” — Lindsey Graham on “Sunday Morning Futures With Maria Bartiromo,” May 12, 2019 “ You guys know what it’s like. This is a walking invasion. Where’s the action? ” — Brian Kilmeade on “Fox & Friends,” June 3, 2019 “ Calling it anything but an invasion at this point is just not being honest with people. ” — Laura Ingraham on “The Ingraham Angle,” July 10, 2019 Here are three dozen instances on Fox News when immigration along the Mexican border was discussed in terms of an invasion. In November 2018 — as Republicans, who were facing a tough midterm election, pushed the notion of a migrant “caravan” — references to immigrants as invaders came up on more than three shows a day on average. “Calling it anything but an invasion at this point is just not being honest with people,” Laura Ingraham, host of “The Ingraham Angle,” said on her show on July 10. Days after the shooting, the “Fox & Friends” co-host Brian Kilmeade dismissed a connection between words used by the gunman and by President Trump, saying: “If you use the term ‘invasion,’ that’s not anti-Hispanic. It’s a fact.”

In the four years since Mr. Trump electrified Republican voters with slashing comments about Muslims and Mexicans, demonizing references to immigrants have become more widespread in the news media, the Times review found.

Sometimes the hosts are repeating the president’s signature phrases. Sometimes the president appears to take his cues from television pundits. The cumulative effect is a public dialogue in which denigrating sentiments about immigrants are common.

Before the first groups of Central American migrants received heavy news media coverage in 2018, words like “invaders” or “invasion” were rarely used by American outlets. In the last year, the use of such terms has surged, with references to an immigrant “invasion” appearing on more than 300 Fox News broadcasts. The vast majority of those were spoken by Fox News hosts and guests, but some included clips of Mr. Trump using that language at rallies and other public appearances.

The Times analysis examined the last five years of show transcripts from Fox News, CNN and MSNBC to measure the frequency of terms like “invasion” and “replacement.” Segments that included this language were verified by watching clips of the shows to determine whether hosts and guests were speaking in their own words or reporting on the language of others.

“It’s a bit of a vicious cycle,” said the conservative writer William Kristol, a Republican critic of Mr. Trump’s who has worked at Fox News and other networks. “Something is said on Fox News, and Trump repeats it, and that legitimizes it — and then someone else goes a little further.”

He added, “The use of what once would have been viewed as really extreme and inappropriate and sometimes conspiratorial, sometimes dehumanizing language is really striking.”

While the notion of immigrants as a national threat was a feature of the conservative Patrick Buchanan’s unsuccessful bids to win the Republican presidential nominations in 1992 and 1996 (he used the phrase “illegal invasion” then), they ran counter to the Republican Party’s efforts to make itself more appealing to Hispanics and other minorities in the two decades before Mr. Trump became its front-runner.

The portrayal of immigration as a menace has returned with force, a shift brought on not just by radio and TV hosts, but by Republican leaders in Congress and the president himself. This year Mr. Trump has used the terms “invasion” or “invaded” seven times on Twitter to describe the situation at the border, at one point referring to the approach of the migrants as “the attempted Invasion of Illegals.” At rallies, he has injected terms like “predator,” “killer,” and “animal” in his descriptions of immigrants.

The Trump-friendly media world — from outlets like Sinclair Broadcast Group and The Drudge Report to platforms like Breitbart News and Gateway Pundit — has used similar incendiary rhetoric. “The fact of the matter is that this is an attempted invasion of our country — period,” Boris Epshteyn, a former Trump campaign adviser, said last year in a commentary on migrants that aired on nearly 200 Sinclair television stations.

At the start of the El Paso suspect’s screed, he refers to the “great replacement,” a white supremacist conspiracy theory based on a French book that claims the migration of minority groups can lead to a “genocide” of white culture.

The El Paso suspect, who confessed to the mass shooting last week, claimed in the document he posted to be defending against a “Hispanic invasion of Texas.” The words “invasion” and “invaders” appear six times in the text, a stark parallel to the language heard on conservative television and talk radio today.

Before the El Paso shootings, others with deadly or hateful motives used the same language.

The replacement theory was prominent in a document posted on 8chan by the suspect in the massacre that killed 51 people in a mosque in Christchurch, New Zealand, in March.

The man who is alleged to have killed 11 people in a Pittsburgh synagogue last October had expressed his contempt for “invaders” before he opened fire on the congregation with an AR-15-style assault rifle, the authorities say. During the white supremacist demonstrations in Charlottesville, Va., in 2017 that left one woman dead, marchers shouted, “You will not replace us.”

Lawrence Rosenthal, a professor at the Berkeley Center for Right-Wing Studies, said that the shared vocabulary of white nationalists and many prominent conservatives was chilling. “Where that intersects with the Republican Party today,” he added, “is the Republican argument that the Democrats are in favor of immigration because that will give them a permanent majority.”

Mr. Limbaugh, whose syndicated radio show has a weekly audience of 15 million, has trafficked in similar themes.

“ So here we’ve got hundreds of people flooding our southern border claiming refugee status. ” — “The Rush Limbaugh Show,” Aug. 12, 2013 “ When you flood the country with millions of people who are predestined to vote Democrat, in a vast majority sense, who are inexperienced and low wage, what in the world is going to happen? When you bring in that many or legalize that many and you’ve given up your assimilation, the assimilation aspect of immigration? ” — “The Rush Limbaugh Show,” Jan. 30, 2014 “ So now the regime is considering a plan to stem the surge of migrants, but what instead is actually going to happen — and any fool should know this — this is going to encourage a flood of new illegal immigrants to try their luck using the refugee excuse. ” — “The Rush Limbaugh Show,” July 25, 2014 “ Meanwhile, the flow of illegal immigrant children into the U.S. is expected to rise this year. Record breaking numbers. This is an untold story. We think it was the story of last year, where you had all these minors from Central America flooding the border, and they were. ” — “The Rush Limbaugh Show,” Feb. 24, 2016 “ If just threatening to enforce the law has slowed the flood of illegal immigrants, think what actually enforcing it will do. ” — “The Rush Limbaugh Show,” April 11, 2017 “ And Trump is exactly right. They do want the country flooded with illegal immigrants and refugees. ” — “The Rush Limbaugh Show,” Nov. 28, 2017 “ You think it’s not an immigration issue; it is. Their express purpose is to flood the United States. Their express purpose is to storm the border and flood in. ” — “The Rush Limbaugh Show,” Oct. 23, 2018 “ They’re headed this way, and if the flood is not stopped, this is all — it’s gonna become demographically axiomatic after a while. It has to be stopped. It has to be stopped. ” — “The Rush Limbaugh Show,” Jan. 21, 2019 “ I think they’re gonna continue to flood the border no matter what Trump does because I think this is all politics. I don’t think that the root of this is people escaping disease and poverty and what have you. ” — “The Rush Limbaugh Show,” March 6, 2019 “ There’s something behind this, folks, all these caravans amassing. This just doesn’t happen organically. This is part of a targeted political project to flood this country and to paralyze the Trump administration. ” — “The Rush Limbaugh Show,” April 2, 2019 “ They want the illegal immigrants, and they want the flood. They want invasion because they don’t like America, and they want to restructure America and erase all aspects of the founding. ” — “The Rush Limbaugh Show,” April 15, 2019 “ My memory is there are three different funding organizations with U.S. dollars and U.S. organizations that are behind the assemblage of these caravans, including the drug cartels and human traffickers who are attempting to participate in this swarming and flooding of the border. ” — “The Rush Limbaugh Show,” July 16, 2019 Mr. Limbaugh has repeatedly described the flow of migrants across the Mexico border as a flood that will overtake America with cheap labor and dilute the country’s identity.

On Wednesday, responding to the El Paso shootings, Mr. Limbaugh said, “What is it about the word ‘invasion’ that so bothers these people? Is it because that’s what it is? Have we ever seen anything like this?”

On Fox News, Mr. Carlson has proffered a version of this idea, albeit in less extreme language than that of the 8chan message boards where the El Paso killer lurked.

“ Their political success does not depend on good policies but on demographic replacement, and they’ll do anything to make sure it happens. ” — Tucker Carlson on “Tucker Carlson Tonight,” Dec. 20, 2017 “ Have they ever proposed shutting the government down to protest on behalf of American workers? Who’ve been harmed by immigration policies that have replaced them with cheap foreign labor? ” — Michelle Malkin on “Fox & Friends,” Jan. 19, 2018 “ This is really destroying one culture and replacing it with the new foreign culture. ” — Tucker Carlson on “Tucker Carlson Tonight,” Aug. 3, 2018 “ Of this my friends you can be sure — your views on immigration will have zero impact and zero influence on a House dominated by Democrats who want to replace you, the American voters, with newly amnestied citizens and an ever increasing number of chain migrants. ” — Laura Ingraham on “The Ingraham Angle,” Oct. 16, 2018 “ I’m not against the immigrants. I’m just — I’m for Americans, and nobody cares about them. It’s like, shut up, you’re dying. We’re going to replace you. ” — Tucker Carlson on “Tucker Carlson Tonight,” Dec. 4, 2018 “ So our plan here in the West is to just let the depressed people die off and replace them with people from other countries. What do you think of that plan? ” — Tucker Carlson on “Tucker Carlson Tonight,” Feb. 13, 2019 “ If the city’s unemployment rate is high, it’s just more proof that they deserve replacement by foreign workers of some kind. ” — Tucker Carlson on “Tucker Carlson Tonight,” March 4, 2019 “ We need to stop viewing struggling Americans as defective people who deserve to be replaced by superior foreign immigrants — the Pelosi model. ” — Tucker Carlson on “Tucker Carlson Tonight,” May 17, 2019 Mr. Carlson’s shows routinely feature discussions of being replaced by immigrants.

Mr. Carlson, whose show averages about three million viewers a night, has featured guests who subscribe to the replacement theory, like Peter Szijjarto, the foreign minister to Hungary’s nationalistic president, Viktor Orban. In February, Mr. Carlson and Mr. Szijjarto discussed the need to increase birthrates in their respective countries. Otherwise, Mr. Carlson said, “our plan here in the West is to just let the depressed people die off and replace them with people from other countries.”

Another prime-time Fox News host, Laura Ingraham, who was considered for a communications job in the Trump administration, has used similar language. Last October, she warned viewers that their opinions “will have zero impact and zero influence on a House dominated by Democrats who want to replace you, the American voters, with newly amnestied citizens and an ever-increasing number of chain migrants.”

Fox News had no comment.

The overlap between fringe ideology and the words of conservative talk show hosts is not accidental, critics say. “They’re putting that into the zeitgeist,” said Carl Cameron, the former chief political correspondent for Fox News, who is now working for a news aggregator aimed at a progressive audience, Front Page Live.

“Fox goes out and looks for stuff that is inherently on fire and foments fear and anger,” Mr. Cameron added.

The use of “invasion” and “invaders” has also surfaced on outlets away from right-wing media. The Times review of demonizing terms for immigrants found a spike in such terms in 2018 on CNN and MSNBC, but almost exclusively in the context of reporting how leading conservatives had been using such language.

Fox News, it should be noted, is not monolithic. While its prime-time lineup of Mr. Carlson, Sean Hannity and Ms. Ingraham is devoted to right-wing commentary, some of the network’s news reporters, like the anchor Shepard Smith, have taken pains to refute misleading language about migrants. Chris Wallace, the “Fox News Sunday” host, recently grilled the White House chief of staff, Mick Mulvaney, about the racism inherent in Mr. Trump’s critical remarks about Baltimore.

Days after the El Paso massacre, Mr. Carlson said on-air that white supremacy was “actually not a real problem in America” and likened it to a “hoax.” His words ignited widespread criticism, including from fellow conservative commentators like Erick Erickson and a Fox News weekend anchor, Arthel Neville.

The next night, Mr. Carlson returned to his show and urged his critics to “calm down,” warning about the roiling divisions in the country, before announcing that he was leaving on a vacation that he and Fox News said had been previously planned.