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Enrique Pena Nieto said he "lamented" the plans for the barrier, adding that "Mexico doesn't believe in walls".
But he made no mention of cancelling or postponing a trip to Washington on 31 January to meet the new US president.
Mr Trump has signed an executive order for an "impassable physical barrier" and has insisted Mexico would reimburse the US for it.
Mr Pena Nieto said: "I've said time and again; Mexico won't pay for any wall.
In 2014, Mexico received a total of $332,311,612 in foreign assistance from the U.S. That breaks down into $281,093,177 in economic assistance and $51,218,435 in military assistance.