The White House claimed Monday that Canada "caved" to President Donald Trump by hastily rescinding its digital services tax after the president threatened to shut down trade negotiations between the two major trading partners.

"It's very simple: Prime Minister [Mark] Carney and Canada caved to President Trump and the United States of America," press secretary Karoline Leavitt told reporters at a briefing.

"It was a mistake for Canada to vow to implement that tax that would have our tech companies," Leavitt said.

Carney, she added, called Trump Sunday night to "let the president know that he would be dropping that tax, which is a big victory for our tech companies and our American workers."

Neither the office of the prime minister nor his Liberal Party immediately responded to CNBC's requests for comment.

Leavitt's remarks came hours after top Trump economic aide Kevin Hassett said the White House will likely ask more countries to drop their own digital services taxes as part of ongoing trade talks, following Canada's concession.

"My expectation is that the digital services taxes around the world will be taken off, and that that will be a key part of the ... ongoing trade negotiations that we have," Hassett, the director of Trump's National Economic Council, said on CNBC's "Squawk on the Street."

The remark from Leavitt and Hassett came one day after Canada walked back its DST in order to "advance broader trade negotiations" with the United States.

That reversal — just hours before the first collection under the new tax was due — came on the heels of Trump's surprise threat Friday to terminate all trade talks with Ottawa as long as the DST remained in place.

Canada said negotiations with the U.S. have resumed since it scrapped the tax. Trump and Canadian Prime Minister Mark Carney now aim to strike a trade deal by July 21, according to a statement Sunday from the Department of Finance in Ottawa.

"I'm very pleased to see that Canada is removing its DST, which means that we didn't have to put in this really complicated retaliation to the tax code," Hassett said Monday.

"But you could expect that countries that have digital sales taxes of the future are going to be facing the wrath of [U.S. Trade Representative] Jameson Greer" over "these unfair trade practices," Hassett said.

In a little over a week, the Trump administration's steep tariffs on imports from a number of countries are set to restart.

Hassett said he believes the U.S. has "frameworks" for "a whole number of deals" that will be agreed to shortly after a major Trump-backed budget bill passes through Congress.

The Trump administration is eager for the GOP-controlled House and Senate to pass a final version of the massive tax-and-spending legislation and send it to the president's desk before Friday.

If that happens, Hassett predicted, there will be a "marathon session" in the Oval Office in which Trump and his aides will tick down a list of countries and make final calls on U.S. tariff rates for each.

It is unclear whether Trump will stick to the July 8 and July 9 tariff deadlines. "We can do whatever we want," he said Friday when asked whether he would stick with one of those dates.