President Trump would find broad public support for declaring a national emergency over gun violence, late-night talk show host Stephen Colbert predicted.

The “Late Show” host made the assumption during an interview Thursday with actor Bradley Whitford while discussing the possibility of the president declaring a national emergency to kick-start construction of a contentious wall he campaigned on building at the Mexican border.

“There is an emergency in this country,” Mr. Whitford said during the segment. “40,000 American citizens die. Over 10 times the number of the people who died in 9/11 die every year from gun violence in this country. There is an emergency.”

“I think if the president declared an emergency over that, the vast majority of Americans would agree,” Mr. Colbert responded.

Mr. Trump has proposed building a wall since the start of his 2016 election campaign, and he said Thursday that he has an “absolute right” to expedite construction by declaring a national emergency at the Mexican border, potentially resolving a dispute at the center of an ongoing partial government shutdown that started roughly three weeks earlier.

The president refrained from rushing to act, however, later telling reporters at the White House: “I’m not going to do it so fast.”

“What we’re not looking to do right now is national emergency,” Mr. Trump said Friday.

The president has refused to sign a bill funding the federal government unless it allocates billions of dollars toward building the proposed border wall, triggering the shutdown currently tied as the longest in U.S. history.

A total of 39,773 people were killed by guns in the U.S. 2017 — about 10 times the nearly 3,000 who died as a result of the Sept. 11 terrorist attacks in 2011, The New York Times reported last month.

“If we really want to start talking about a national emergency like the president likes to talk about, 40,000 Americans dying annually from gun violence is a pretty damn good one to start out with — because it is an issue that is nonpartisan,” shooting survivor and activist David Hogg, 18, told CNN on Tuesday. At least I would hope so, considering the fact that both Democrats and Republicans die from gun violence. Bullets don’t discriminate and neither should our legislators.”

Mr. Whitford, a 59-year-old Emmy Award winner, echoed the activist during his subsequent appearance on Mr. Colbert’s CBS program.

“What I’m saying about the Republicans, what I don’t understand, is apparently their view is children being slaughtered in schools with weapons of war is part of the cost of freedom, but universal background checks is too high a price to pay,” Mr. Whitford said. “It’s insane, and we have to get back to a sense of fact-based sanity in this country.”