World :: Mexico 'will not pay for Trump wall'
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 will reimburse the US for it.
Mr Pena Nieto told the nation in a televised address: "I've said time and again; Mexico won't pay for any wall.
"I regret and condemn the decision of the United States to continue construction of a wall that, for years, has divided us instead of uniting us."
But Mr Pena Nieto said his country offered "its friendship to the American people and its willingness to reach accords with their government".
Mexican Foreign Minister Luis Videgaray - in Washington to lead a delegation that has held talks at the White House - told the Televisa network the president was still weighing next Tuesday's visit but said "the meeting stands for now".