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.
"It comes as our country is talking on new rules on cooperation, trade, investment, security and migration in the North American region.
"As president I assume the complete responsibility to defend the interests of Mexico and Mexicans.
"Based on a final report by the functionaries in Washington DC and advice from the chamber of commerce, governors, and so on, I will decide the right next steps to take.
"Mexico offers its friendship to the American people and its willingness to reach accords with their government. Agreements that will be in favour of both Mexico and the US."
Recall that Mr Trump said in a TV interview with ABC News that Mexico would "absolutely, 100%" reimburse the US for his wall.