"A nation without borders is not a nation" says Donald Trump.
Mexico will not pay for Donald Trump's border wall, the country's president has said in a message to the nation.
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".
Mr Pena Nieto met Mr Trump - then a presidential candidate - in Mexico City in September and came under intense criticism at home and his current approval ratings are low.
Mr Trump said in an interview with ABC News that Mexico would "absolutely, 100%" reimburse the US for his wall. But Congress would have to approve funding for the structure, which is estimated to cost billions of dollars.
Building a 2,000 mile (3,200km) barrier along the Mexican border was one of Mr Trump's key pledges in the election campaign.
He spoke of a "crisis" on the southern US border as he signed the directives during a ceremony at the Department of Homeland Security on Wednesday. The orders also called for hiring 10,000 immigration officials to help boost border patrol efforts.
"A nation without borders is not a nation," he said. "Beginning today the United States gets back control of its borders."
