As he spoke to journalists on Wednesday, Mr Trump brandished a piece of paper which contained details of an agreement with Mexico created to limit tariffs if the country can better control migration into the US.
He refused to discuss the plans with reporters, saying they were "secret". The document has language suggesting that Mexico might consider changing its laws to facilitate a regional "safe third party" asylum system, subject to "domestic and global legal obligations", in which migrants would have to apply for asylum in the first country they enter.
If the agreement fails, Mexico said it would consider becoming a "safe third country".
But he said this while waving around a sheet of paper that had the specifics of the deal written on it - which was then photographed by news media.
Ebrard said Mexico implemented a working group with Guatemala, Honduras and El Salvador to coordinate efforts at stemming the tide of people fleeing violence and poverty in Central America.
It also mentioned "45 days" and said Mexico agreed to examine its laws regarding the introduction an agreement on asylum seekers into the US.
Speaking during a press briefing on Wednesday, Foreign Minister Marcelo Ebrard said the roll-out of some 6,000 troops across its border with Guatemala had commenced and would "progress rapidly" over the "coming days".
"The idea is to make the south like the north as far as possible".
Mr Ebrard earlier said the USA had been insistent on this measure, and that they had wanted this to be implemented straight away.
"Right now Mexico is helping us more on immigration than the Democrats in the USA, the president said. We have been trying to get some of these Border Actions for a long time, as have other administrations, but were not able to get them, or get them in full, until our signed agreement with Mexico", Trump tweeted. But that is what there is here. "There is no other thing", he said.
Mr Ebrard also said USA negotiators had wanted Mexico to commit to "zero migrants" crossing its territory, but that was "mission impossible".