Marcelo Ebrard also said they would try reinforcing their southern border to deliver the swift reduction in migrants demanded by US President Donald Trump.
Mexico has 45 days to reduce the number of US-bound migrants crossing its territory, or else face US tariffs.
Even though no specific target has been set, Mr Ebrard said these measures would be evaluated in mid-July.
If the number was not down by then, discussions would take place with Brazil, Panama and Guatemala - the countries currently used by migrants as transit points.
Mr Ebrard said the agreement reached with the US on Friday after days of "most difficult negotiation" bought Mexico time to show it could succeed in driving down the number of migrants.
He said that US negotiators had wanted Mexico to commit to "zero migrants" crossing its territory, but according to Mr Ebrard, that was "mission impossible".
Mr Ebrard said the US side also wanted to designate Mexico as a "safe third country", which would have required Mexico to take in asylum seekers heading for the US and process their claims on its own soil.
The foreign minister said that he had averted that measure for the time being: "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'".
Mexico said it would deploy its National Guard throughout the country from Monday with 6,000 additional troops being sent to its southern border with Guatemala.
Illegal border crossings on Mexico's northern border with the US have been on the rise again after reaching a low in US President Donald Trump's first year in office.
In February, Mr Trump declared an emergency on the US-Mexico border, saying it was necessary in order to tackle what he described as a crisis.
In May, Mr Trump threatened that 5% tariffs on Mexican goods would be imposed on 10 June and rise by 5% every month until reaching 25% in October if Mexico did not take substantial action to curb migration.
Mexico is currently one of the largest trading partners for the US, just behind China and Canada. After days of negotiations, a deal was reached on Friday which both sides hailed as a success.
But on Monday, President Trump warned that tariffs were not off the table completely, saying that if the part of the deal which required approval by Mexico's congress was not passed, the tariffs would be reinstated.