STERLING, Va. — President Donald Trump on Sunday dangled the prospect of renewing his tariff threat against Mexico if the U.S. ally doesn't cooperate on border issues, while some of his Democratic challengers for the White House said the last-minute deal to avert trade penalties was overblown.

In a series of tweets, Trump defended the agreement heading off the 5 percent tax on all Mexican goods that he had threatened to impose Monday, but he warned Mexico that, “if for some unknown reason” cooperation fails, “we can always go back to our previous, very profitable, position of Tariffs.”

Still, he said he didn't believe that would be necessary.

The tweets came amid questions about just how much of the deal — announced with great fanfare Friday — was really new. It included a commitment from Mexico, for instance, to deploy its new National Guard to the country's southern border with Guatemala. Mexico, however, had already intended to do that before Trump's latest threat and had made that clear to U.S. officials.

“We want to continue to work with the U.S. very closely on the different challenges that we have together. And one urgent one at this moment is immigration,” said Mexico's ambassador in Washington, Martha Barcena.

She told CBS' “Face the Nation” that the countries' “joint declaration of principles ... gives us the base for the road map that we have to follow in the incoming months on immigration and cooperation on asylum issues and development in Central America.”