But officials from both countries said the two sides reached no commitment on such a treaty, and they said the provisions that were included in the deal were essentially reaffirmations of actions Mexico had already agreed to in previous discussions. American officials argued privately that the value of the agreement may be greater dedication by Mexico to actually follow through on such commitments to avoid another threat of tariffs by Mr. Trump.

Kevin K. McAleenan, the acting secretary of homeland security, said the agreement did advance Mexico’s commitment to fighting border crossings beyond previous discussions, citing in particular a promise to deploy a newly formed national guard to its own southern border as well as elsewhere in the country.

“All of it is new,” Mr. McAleenan said on “Fox News Sunday.” “I mean, we’ve heard commitments before from Mexico to do more on their southern border. The last time they deployed down there is about four or five hundred officers. This is more than a tenfold commitment to increase their security in Chiapas. That’s where people are entering from Guatemala and southern Mexico.”

Mr. McAleenan did not explain Mr. Trump’s tweets except to say that the two countries would continue to talk about what they could do to combat illegal immigration. “There are going to be further actions, further dialogue with Mexico in immigration, on how to manage the asylum flow in the region,” he said.

While critics questioned the value of the deal after Mr. Trump called off the new tariffs, Mr. McAleenan said the threat made a difference. “People can disagree with the tactics,” he said. “Mexico came to the table with real proposals.”

But the two sides offered divergent descriptions of what would count as success. Mr. McAleenan said Mexico’s actions had to result in “a vast reduction in those numbers” of people crossing the border, which reached a 13-year high in May. But Mexico’s ambassador said the goal was to have the numbers “go down like to previous levels that we had maybe last year or in 2018.”

Ambassador Martha Bárcena Coqui said Mexico had already been deploying its national guard but would increase it starting on Monday. She described the agreement as less concrete and more of a start to a more precise accord.