Steven Mnuchin, Secretary of the Treasury of the United States of America, during a G-20 meeting on June 08, 2019 in Fukuoka, Japan.

Treasury Secretary Steven Mnuchin said Sunday that Washington is "very excited" about an agreement with Mexico to help stem the flow of immigrants attempting to enter the U.S., but he warned that the White House could renew its threats of punitive tariffs if it found itself unsatisfied.

That comes after U.S. President Donald Trump announced on Friday that his team had reached an agreement with Mexico to "greatly reduce, or eliminate, Illegal Immigration coming from Mexico and into the United States." In turn, the president withdrew his threat to place levies on Mexican goods.

I am pleased to inform you that The United States of America has reached a signed agreement with Mexico. The Tariffs scheduled to be implemented by the U.S. on Monday, against Mexico, are hereby indefinitely suspended. Mexico, in turn, has agreed to take strong measures to.... ....stem the tide of Migration through Mexico, and to our Southern Border. This is being done to greatly reduce, or eliminate, Illegal Immigration coming from Mexico and into the United States. Details of the agreement will be released shortly by the State Department. Thank you!

Mnuchin said the deal — which The New York Times reported is largely comprised of actions Mexico had already agreed to take — represented an important diplomatic step.

"We're very excited about the Mexico agreement. We very much appreciate the government working with us on immigration — these are very important issues and they've made significant commitments," he told CNBC's Nancy Hungerford.

"The immigration issue was a very serious issue, we couldn't be more pleased that Mexico came to the table and negotiated an agreement, and because of that, we don't need to put tariffs on them," he added.

Still, the Treasury secretary suggested that Trump could readily reinstate his tariff threat if he deems it necessary.

"I have every reason to believe they will meet their commitments, so I think that will be the case, but if for whatever reason they don't, the president reserves the right to put on tariffs," Mnuchin said, echoing comments that had previously been reported by Reuters.

The Trump administration official also addressed the complaints that some have made about mixing tariffs — a tax on trade — with non-trade issues. He, for one, suggested there was no problem in using such levies to address a range of problems.

"I think it's very important that we have all these tools, that we use them," Mnuchin said. "And President Trump has really done a great job in using these tools."