The Mexican newspaper Reforma first published the letter, signed and dated June 7, which the US president carried when he said there was a secret agreement.
It states that the US and Mexico "will immediately begin discussions to establish definitive terms for a binding bilateral agreement to further address burden-sharing and the assignment of responsibility for processing refugee claims of migrants."
There was no other agreements from the negotiations with the US, said Mexican Foreign Minister Marcelo Ebrard, while presenting the document to the Mexican Senate on Friday.
It further states that the two countries would commit to "accept the return and process refugee status claims, of third-party nationals who have crossed that party's territory to arrive at a port of entry or between ports of entry of the other party."
Mexico will have another 45 days to bring the agreement into force if its measures "have not sufficiently achieved results in addressing the flow of migrants to the southern border," adds the letter.
After the deal was unveiled and Trump’s threat of tariffs was cancelled, reports said that Mexico had agreed to the deal months earlier.
"That’s the agreement that everybody says I don’t have," Trump told reporters at the White House on Tuesday while pulling the document from the pocket of his blazer. "This is one page of a very long and very good agreement for both Mexico and the United States."
Washington and Mexico reached an accord to avoid a tariff war on Friday after Mexico agreed to expand a controversial asylum program and dispatch its security forces to contain the flow of illegal immigration from Central America.