Washington (CNN) President Donald Trump delivered another litany of false and misleading claims on Monday at a White House coronavirus briefing during which he repeatedly accused the media of dishonesty.

Trump delivered an indignant screed about claims that he was slow in responding to the coronavirus outbreak, repeatedly citing the travel restrictions on China he announced in late January and began in early February. Yet his defense did not address his public downplaying of the virus into March, how his administration was slow to deploy the tests experts believe might have helped contain the outbreak, or how the administration waited critical weeks to make large orders of critical equipment.

Trump also falsely claimed he has "total" authority over states' coronavirus restrictions, falsely claimed he had inherited broken coronavirus tests, falsely claimed presumptive Democratic nominee Joe Biden apologized for having called him xenophobic, falsely claimed that governors have stopped talking about a need for ventilators, and falsely claimed he banned travel from Europe.

Here's our preliminary rundown of his claims and the facts that go with them. This will be updated throughout the night.

Fact checking a portion of the White House video presentation

During the task force briefing, the White House presented a digital montage of TV and radio clips of Trump's early actions with the coronavirus. One clip featured audio from New York Times reporter Maggie Haberman, who can be heard describing how the President was criticized for his early travel ban from China.

Facts First: The Haberman quotes are misleading as they edit out one of her key points: that the President's travel restriction was one of the last actions he took to address the coronavirus for weeks.

Here's the Haberman quote as it was presented by the White House video:

"As there were more cases and it was clear that it was spreading out of China -- where it originated -- the President took this move that he was widely criticized for by Democrats and even some Republicans at the time. Which was he halted a number of flights from China into the U.S. The idea was to halt the spread of the disease, keep transmissions to a minimum. He was accused of xenophobia. He was accused of making a racist move. At the end of the day, it was probably effective, because it did actually take a pretty aggressive measure against the spread of the virus."

According to a transcript of The Daily podcast from March 25, here's the end of the quote, including a key point (in bold) at the end that was left out of the White House presentation:

"At the end of the day, it was probably effective, because it did actually take a pretty aggressive measure against the spread of the virus. The problem is, it was one of the last things that he did for several weeks."

According to the transcript, the Daily's host Michael Barbaro asked a follow up question: "So the right decision in retrospect, but not accompanied by similar actions that might have contained transmission."

Haberman responded: "That's exactly right. In the same way that George W. Bush was criticized for his 'Mission Accomplished' banner about Iraq, the President treated that moment as if it was his mission accomplished moment. He did not do anything after that in terms of alerting the public, or telling people to be safe, or telling people to take precautions. And it basically squandered several weeks within the US."

As Haberman pointed out on Twitter , she went on to say that the President "treated that travel limitation as a Mission Accomplished moment," harkening back to former President George W. Bush.

Joe Biden and the travel restrictions on China

Trump claimed that presumptive Democratic presidential nominee Joe Biden has apologized for having accused him of xenophobia on January 31, when Trump's administration announced its coronavirus travel restrictions on China.

"He has since apologized and he said I did the right thing," Trump said.

Facts First: Biden has not apologized for having called Trump xenophobic. Furthermore, it's not clear the former vice president even knew about Trump's China travel restrictions when he called him xenophobic on the day the restrictions were unveiled.

Biden's campaign announced in early April that he supports Trump's travel restrictions on China, so part of Trump's Monday claim is correct. But the Biden campaign did not say the former vice president had previously been wrong about the ban, much less apologize. Rather, the campaign says Biden's January 31 accusations -- that Trump has a record of "hysterical xenophobia" and "fear mongering" -- were not about the travel restrictions at all.

The campaign says Biden did not know about the restrictions at the time of his speech, since his campaign event in Iowa started shortly after the Trump administration briefing where the restrictions were revealed by Health and Human Services Secretary Alex Azar.

Given the timing of the Biden remarks, it's not unreasonable for the Trump campaign to infer that the former vice president was talking about the travel restrictions. But Biden never took an explicit position on the restrictions until his April declaration of support -- and whether or not you accept his campaign's argument that the "xenophobia" claim was not about the restrictions, he certainly hasn't apologized for the accusation.

Coronavirus testing

At Monday's briefing, Trump implied that he had inherited flawed coronavirus tests from President Barack Obama's administration.

"We literally rebuilt tests -- we rebuilt a whole industry because we inherited nothing," Trump said. "What we inherited from the previous administration was totally broken, which somebody should eventually say. Not only were the cupboards bare, as I say, but we inherited broken testing. Now we have great testing."

Facts First: Since this is a new virus that was first identified this year, the tests for it are newly created, not inherited from the Obama administration. The faulty initial test for the coronavirus was created during Trump's administration, in early 2020, by the Centers for Disease Control and Prevention.

The claim "doesn't make sense because it is false," Tara Smith, an epidemiology professor at Kent State University, said of a previous version of Trump's claim. "This a new virus."

"He is lying. He is lying 100%. He is lying because he is trying to shift blame to others, even if the attempt is totally nonsensical," Gregg Gonsalves, an assistant professor in the Department of Epidemiology of Microbial Diseases at the Yale School of Public Health, said of a previous version of the claim.

Trump has made versions of this claim on multiple occasions, shifting his rhetoric over time from a broader and more debatable claim that the testing "system" was flawed. While his Monday claim about having inherited "broken testing" is slightly vaguer than his claims about having inherited faulty or obsolete "tests," it creates the same impression.

You can read more here about the President's various claims on inheriting tests.

President has 'total' authority over coronavirus restrictions

Trump falsely claimed on Monday that, as President, he has "total" authority to decide to lift restrictions governors have imposed to fight the coronavirus pandemic.

"When somebody's the President of the United States, the authority is total, and that's the way it's got to be," Trump said at the White House coronavirus briefing.

Trump then said: "The authority of the President of the United States having to do with the subject we're talking about is total." And after speaking about local governments, he said, "They can't do anything without the approval of the President of the United States."

It wasn't clear if he was referring to state or local officials with that assertion. But he was wrong regardless.

Facts First: The President does not have "total" authority over coronavirus restrictions. Without seeking or requiring Trump's permission, governors, mayors and school district officials imposed the restrictions that have kept citizens at home and shut down schools and businesses, and it's those same officials who have the power to decide when to lift those restrictions. There is no legislation that explicitly gives the President the power to override states' public health measures. In addition, Trump said last week that he prefers, because of the Constitution, to let governors make their own decisions on coronavirus restrictions.

We can't say for sure that the courts would not side with Trump if he attempted to challenge state restrictions on some constitutional grounds he has not yet identified. However, many legal scholars believe Trump would lose.

James Hodge, a professor and director of the Center for Public Health Law and Policy at Arizona State University, said Trump is "wrong" to claim he has the power to lift the states' coronavirus restrictions.

"He can strongly encourage, advise, or even litigate whether states' authorities to restrict public movements re: shelter in place or stay home orders are warranted, but cannot tell sovereign governors to lift these orders all at once just because the federal government determines it is high time to do so," Hodge said in an email.

Trump's Monday evening comments at the briefing echoed tweets from earlier in the day in which he asserted that "it is the decision of the President," not governors, on when to "open up the states."

"This tweet is just false. The President has no formal legal authority to categorically override local or state shelter-in-place orders or to reopen schools and small businesses. No statute delegates to him such power; no constitutional provision invests him with such authority," Stephen Vladeck, a University of Texas law professor and CNN legal analyst, said on Twitter on Monday.

Trump did not personally shut down the economy. Rather, he issued nonbinding guidelines on how people should keep their distance from each other. The guidelines begin as follows: "Listen to and follow the directions of your STATE AND LOCAL AUTHORITIES."

No legislation says the President has the power to overturn the public health decisions of these authorities, Vladeck and other legal scholars say.

Trump did not explain why he believes he has this power. When CNN's Kaitlan Collins asked him who told him he has "total" authority, he did not answer directly, instead saying, "We're going to write up papers on this."

When another reporter explained that the Tenth Amendment to the Constitution grants to states the powers not delegated to the federal government, Trump did not contest this interpretation -- and instead sidestepped the question, saying he did not believe a state official who refused to reopen the economy could win reelection.

Trump-friendly website Breitbart broached the possibility that Trump could try to use the Constitution's Commerce Clause, which gives Congress the power to regulate interstate commerce, to try to lift commercial restrictions.

Robert Barnes, a lawyer who supports Trump, argued to CNN on Monday that, "in the emergency context," the President possesses these commerce powers the Constitution assigns to Congress.

Vladeck said Barnes' claim is unfounded. While Vladeck said Congress might be able to pass a law authorizing the President to override some state and local restrictions -- he emphasized the "might" -- he said Trump does not have the power to override the restrictions on his own.

"Congress has delegated the President a bunch of powers for emergencies, but this isn't among them," Vladeck told CNN.

Hodge said states have a l ong-established authority to restrict some commerce for the protection of public health. And it is widely understood that state governments have the power to address public health emergencies within their states.

In a 2014 report , the Congressional Research Service, which provides nonpartisan research and analysis to Congress, looked at federal and state powers over quarantine and isolation. The report did not specifically address the question of a president wanting to override state public health measures, but it noted: "In general, courts appear to have declined to interfere with a state's exercise of police powers with regard to public health matters 'except where the regulations adopted for the protection of the public health are arbitrary, oppressive and unreasonable.'"

While both the Congressional Research Service report and the National Conference of State Legislatures say that the federal government can "take over" the management of a public health incident within a state "if the federal government determines local efforts are inadequate," they do not specifically address a situation in which the federal government wants to take over because it believes the state is being too strict in trying to address the emergency.

Trump has some power

Trump himself has spoken as recently as last week about states' constitutional powers during the pandemic, though he has asserted that he too has powers.

After he was asked on April 10 about the possibility of Florida's governor opening up schools in May, the President said: "I like to allow governors to make decisions without overruling them, because from a constitutional standpoint, that's the way it should be done. If I disagreed, I would overrule a governor, and I have that right to do it. But I'd rather have them -- you can call it 'federalist,' you can call it 'the Constitution,' but I call it 'the Constitution.' I would rather have them make their decisions."

Trump does have some clear, though limited, direct power. For example, he can order federal employees to return to their offices and reopen national parks and other federal property.

And he can, obviously, use his influence to try to persuade governors -- and citizens -- to do as he wishes.

It is also possible that Trump could try to leverage the "major disaster declaration" he has issued for each state -- for example, attempting to require governors to take certain steps in exchange for federal assistance. Hodge, though, said it "could be unconstitutional" to try to impose new conditions for the receipt of federal funding after having already authorized the disaster declarations without such conditions.

Trump also asserted at the briefing that even Democratic governors would agree with his claim to total authority. New York Democratic Gov. Andrew Cuomo, speaking shortly after the briefing to CNN's Erin Burnett, said he disagreed: "We have a Constitution. We don't have a king."

Fact checking Trump's claims about his travel restrictions on Europe, China

Responding to criticism of his administration's response to the coronavirus, Trump touted his decision to limit travel from areas which had more coronavirus cases than the US at the time.

Trump told reporters Monday, "I did a ban on China, you think that was easy? Then I did a ban on Europe and many said it was an incredible thing to do."

Asked later about whether he'd be willing to lift travel restrictions as part of opening up the country, Trump added, "Right now we have a very strong ban. We will keep it that way until they heal."

Facts First: It's misleading to call the travel restrictions Trump announced against China and Europe a ban because they contained multiple exemptions. Only foreign nationals who had been in China, Europe's Schengen area, the UK or Ireland within the past 14 days are outright banned from entering the US.

As of February 2 , US citizens who had been in China's Hubei province in the two weeks prior to their return to the United States are subject to a mandatory quarantine of up to 14 days upon their return to the US. American citizens returning from the rest of mainland China may also face up to 14 days of quarantine after undergoing health screenings at selected ports of entry.

The broader European travel suspension Trump announced on March 11 applied to the 26 countries in the Schengen Area, a European zone in which people can move freely across internal borders without being subjected to border checks. While Trump initially identified the United Kingdom as exempt, additional countries that are not in the Schengen Area and thus also exempt from the restrictions include Ireland, Croatia, Cyprus, Bulgaria, Romania, Ukraine, Serbia, Armenia, Montenegro, Belarus and Russia. As of March 14, the ban was expanded to include foreign nationals traveling from UK and Ireland.

The restrictions also did not apply to US citizens returning from Europe as well as permanent US residents and certain family members of both citizens and permanent residents. You can read more about the European travel restrictions here

Governors have what they need

Trump asserted on several occasions during Monday's briefing that governors across the country are satisfied with his administration's efforts to get states supplies and hospital capacity they need to handle coronavirus patients.

Facts First: Trump's assertions ignore the fact that some governors have said this week that they still need medical equipment and are struggling with hospital bed capacity.

Toward the start of the briefing, the President aired a montage of video clips attempting to frame his administration's response to the coronavirus in a positive light. The montage highlighted clips of numerous governors, both Democrats and Republicans, thanking the President for his administration's assistance.

During the briefing, the President claimed that "no one who has needed a ventilator has not gotten a ventilator."

"If you look, they were all saying, 'We need ventilators,' ... you don't hear ventilators anymore. They have all the ventilators they need. Which we were right about. We said you're asking for too many, you don't need that," Trump said.

In the briefing, Trump also claimed, "No one who has needed a hospital bed has not gotten a hospital bed."

Yet two of the governors included in the montage, New Jersey Gov. Phil Murphy, a Democrat, and Maryland Gov. Larry Hogan, a Republican, just one day prior said that both of their states need more equipment.

"I think to say that everybody's completely happy and that we have everything we need is -- is not quite accurate," Hogan told ABC's "This Week" on Sunday . "I mean everybody still has tremendous needs on personal protective equipment and ventilators and all of these things that you keep hearing about. Everybody's fighting to find these things all over the -- all over the nation and all over the world."

Murphy said Sunday on CNN's "State of the Union" that New Jersey does not have enough supplies to do "universal testing," which is a goal and the state is currently "testing only for symptomatic patients."

Murphy has also said his state is struggling to stay ahead of hospital bed capacity.

"We're fighting to stay ahead on bed capacity, ventilators that are constantly running thin, the medicine you need for those ventilators, the personal protective equipment, and the relief from the bullpen for our health care workers," he added.