Mr Enrique Pena Nieto has said: "I've said time and again; Mexico won't pay for any wall.
Noting that he "lamented" the plans for the barrier, the President had added 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.
In a TV interview with ABC News, Trump had said that Mexico would "absolutely, 100%" reimburse the US for his wall.