The news comes a week into the neighbors' row over tariffs and border security.
But what is known of the agreement has drawn criticism from human rights groups who condemn what they call a draconian crackdown on migration and the criminalization of immigrants.
Mexican officials say they are beginning deployment of 6,000 National Guard troops for immigration enforcement, an accelerated commitment made as part of an agreement with the United States last week to head off threatened USA tariffs on imports from Mexico.
He did not provide details but threatened tariffs if Mexico's Congress did not approve the plan.
It's not Mexico's, but it will go into effect when Mexico tells me it's okay to release it, ' he said of the piece of paper. "If they don't get approval, we'll have to think in terms of tariffs".
"There is no other thing", he said.
But the president appeared to be making a reference to talks over how Mexico handles Central American migrants who travel through the country to claim asylum in the U.S.
"They wanted something else totally different to be signed".
But he said: "We told them - I think it was the most important achievement of the negotiations - 'let's set a time period to see if what Mexico is proposing will work, and if not, we'll sit down and see what additional measures [are needed]'". Okay? If they bring the numbers way down, we won't have to, but this is my option, ' he said.
Asylum seekers from El Salvador and Honduras first pass through Guatemala when fleeing their homes, while Cubans and Haitians often fly first to Panama before heading to the USA through Mexico. I'm not going to say one way or another, ' he said. But when migrants come over, they also hop on rafts.
Washington wants Mexico to be declared a safe third country in which asylum seekers would have to seek safe harbor instead of the United States, a demand Mexico has rejected in the past.
For now, the deal ends plans by the Trump administration to slap a 5 percent tariff on all goods coming into the US from Mexico - something that had sparked fears from both Democrats and Republicans in Congress about the possible economic fallout from such a move.
Ebrard also said there was no agreement between the USA and Mexico to buy more agricultural products under the accord, despite Trump saying over the weekend that Mexico had agreed to buy "large quantities" from USA farmers.
He said the tax on those goods would increase each month the problem persisted until October, when it would cap at 25 per cent.
Last week, the nations signed a last-minute deal to avert the implementation of the tariffs Trump slapped on all Mexican goods.
"This is the first time we've heard anything like this kind of number of law enforcement being deployed in Mexico to address migration, not just at the southern border but also on the transportation routes to the northern border and in coordinated patrols in key areas along our southwest border", McAleenan said on "Fox News Sunday", adding that "people can disagree with the tactics", but "Mexico came to the table with real proposals".
The president called the story "fake news" and insisted the deal was brand new.