White House Chief of Staff Mick Mulvaney said Sunday that the crossing of 1,036 immigrants from Tijuana into the United States in a single incident last week prompted the president’s tariff threat. (Mark Wilson/Getty Images)

The Trump administration sought Sunday to build support for the president’s threat to impose a 5 percent tariff on Mexican imports, despite objections from the U.S. business community and members of his own party.

Conditions “have to get dramatically better, and they have to get better quickly,’’ acting White House chief of staff Mick Mulvaney said on Fox News. “There are specific things the Mexicans can do.’’ The administration, however, has not set any precise immigration reduction targets for Mexico.

Administration officials made the rounds of Sunday television talk shows with a week to go before President Trump’s June 10 deadline to impose the 5 percent tariff on Mexican goods. If Mexico doesn’t stem the flow of immigrants to the United States, the administration has warned, the tariffs would eventually increase up to 25 percent.

Mulvaney said on NBC News’s “Meet the Press” that the catalyst for Trump’s surprise threat last week was the crossing of 1,036 immigrants from Tijuana across the border into the United States in a single incident.

Customs and Border Protection called the early Wednesday breach the largest single detention of migrants to date. The group included 934 family members, 63 unaccompanied minors and 39 single adults, the agency said. Trump tweeted a grainy government surveillance video on Thursday of scores of immigrants filing through an apparent hole in a border fence.

“A group of 1,000 people stormed the border outside of Tijuana, Mexico,’’ Mulvaney said Sunday on NBC. “We’re facing things at the border we’ve never experienced before.’’

He said the mass detention Wednesday “was sort of the touchstone’’ for Trump’s surprise tariff decision.

The time stamp on the surveillance video is 3:20 a.m. Wednesday. Trump issued his threat a little over 24 hours later, sending shock waves through the political world and through securities markets, which took another tumble late last week.

Mulvaney also blamed Democrats in Congress for not supporting Trump’s border agenda, which Mulvaney said caused the president to seek ways to apply direct pressure on Mexico. Democrats have repeatedly rejected billions in funding for Trump’s proposed expansion of a border wall from the Pacific Ocean to the Gulf of Mexico.

“They won’t help us,’’ Mulvaney said.

Trump set off shock and dismay throughout the U.S. business community and from Republicans in Congress with his tariff threat. The criticism from his own party did not let up Sunday. Sen. John Neely Kennedy (R-La.) called Trump’s move a “mistake.”

“He’s been known to play with fire but not live hand grenades,’’ Kennedy said on CBS’s “Face the Nation.’’ “And if he slaps a 25 percent tariff on Mexico, it’s going to tank the American economy, and I think the president knows that, and I don’t think he’ll do it.’’

Trump showed no signs of backing down, however. He kept up the pressure on Mexico on Twitter.

“The problem is that Mexico is an ‘abuser’ of the United States, taking but never giving,’’ the president said in a pair of Sunday morning tweets. “Either they stop the invasion of our Country by Drug Dealers, Cartels, Human Traffickers . . . or our many companies and jobs that have been foolishly allowed to move South of the Border, will be brought back into the United States through taxation (Tariffs). America has had enough!’’

Mexican and U.S. officials are expected to discuss the president’s threat in a meeting in Washington on Wednesday.

Mulvaney and Kevin McAleenan, acting secretary of homeland security, outlined measures that Mexico could take to head off the tariffs.

The administration wants Mexico to crack down on illicit businesses that profit from transporting migrants through the country on their trip north, allow more migrants to seek asylum in Mexico instead of the United States and stop migrants from entering Mexico from Central America in the first place.

“These crossings into Mexico are happening at a 150-mile stretch of their southern border,’’ McAleenan said on CNN’s “State of the Union.’’ “This is a controllable area.’’

The administration also is urging Congress to pass $4.5 billion in a border-related supplemental budget, $3.3 billion of which would be earmarked for improving facilities to house and care for underage migrants, McAleenan said.

Trump’s tariff threat has set off alarm among members of both parties and business leaders, who fear it will damage prospects for a rewrite of the North American trade pact, called the United States-Mexico-Canada Agreement, or USMCA. It also has set off jitters about the potential for disruptive trade battles with other U.S. allies.

Economists have warned about the effect on U.S. consumers of a tax on imports from one of the nation’s most important trading partners.

Mulvaney sought to soothe these concerns. He said the tariff proposal is about immigration, not the broader trading partnership with Mexico, and the administration sees no conflict between the two strategies. He said Trump’s escalating trade war with China has not boosted inflation and tariffs on Mexican imports would similarly not have an effect on prices.

“That old-fashioned economic orthodoxy doesn’t work when it’s relatively easy to substitute other goods,’’ Mulvaney said, predicting a jump in U.S. production of consumer goods to fill the gap. “American consumers will not pay because of the burden of these tariffs.’’

Joseph Marks contributed to this report.