"We do not anticipate a problem with the vote but, if for any reason the approval is not forthcoming, Tariffs will be reinstated!" he added.
Stung by criticism that the agreement mostly ramps up border protection efforts already underway, Trump on Monday hinted at other, secret agreements he says will soon be revealed.
According to the deal, Mexico agreed to deploy 6,000 National Guard troops along its border with Guatemala.
That is different from a long-standing United States demand that Mexico be declared a safe place for asylum seekers, requiring them to seek refuge in Mexico if they passed through the country on the way to the US. "I haven't heard that he is not", Trump said.
"It will go into effect when Mexico tells me it's okay to release it", he said at one point in talking to reporters.
Mr Ebrard said the U.S. had been insistent on this measure, and that they had wanted this to be implemented straight away.
Trump had threatened to impose 5% import tariffs on all Mexican goods from Monday if Mexico did not agree to his demands to tighten its borders. "It will be revealed in the not too distant future and will need a vote by Mexico's legislative body", Trump tweeted.
Ebrard told a news conference on Monday that Trump was referring to possible further measures to pressure countries other than the United States to share the burden.
U.S. State Department spokeswoman Morgan Ortagus said Monday that the two leaders will also discuss ways to strengthen the Washington-Seoul alliance.
"They wanted something else totally different ... to be signed", Ebrard said Monday.
He added later: "We do have one other thing that will be announced at the appropriate time". It also includes an agreement to publicly support the expansion of a program under which some asylum seekers are returned to Mexico as they wait out their cases.
Many had thought Trump was alluding to the idea of Mexico becoming a "safe third country", which would make it harder for asylum seekers who pass through the country from other places to claim refuge in the U.S.
Through the agreement, the U.S.is slated to extend its policy of returning asylum applicants to Mexico while their claims are processed. "They might have accelerated the timetable, but by and large the president achieved nothing except to jeopardize the most important trading relationship that the United States of America has". Mexican officials have described their commitment as an accelerated deployment.
During an interview with Fox and Friends Monday morning, White House Counselor Kellyanne Conway argued Democrats are doing less than Mexican officials to take action.
Expressions by migrants of a fear of returning to their home countries triggers a US immigration court process, which can take months or years to resolve due to backlogs in the system.
"While in theory such an agreement would share the burden of refugee flows across several countries, in reality it could significantly worsen the current situation if the designated countries are unable or unwilling to properly accept and integrate the migrants", she said.
Mexico's President Andrés Manuel López Obrador during a press conference at the National Palace, in Mexico City, on May 31, 2019.