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, but made no mention of changing a scheduled trip to Washington to meet the US president.
Mr Trump responded saying "it would be better to cancel" the 31 January meeting if Mexico is unwilling to pay.
He has signed an executive order for an "impassable physical barrier" and insisted Mexico will reimburse the US.
In a televised address, Mr Pena Nieto told the nation : "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."
He added that "Mexico doesn't believe in walls".
But Mr Pena Nieto said his country offered "its friendship to the American people and its willingness to reach accords with their government".
President Trump took to Twitter following his statement, suggesting Mexico owed the US for the impact of the North American Free Trade Agreement (Nafta).
"The U.S. has a 60 billion dollar trade deficit with Mexico. It has been a one-sided deal from the beginning of NAFTA with massive numbers of jobs and companies lost," he wrote.
"If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting."
Earlier Mexican Foreign Minister Luis Videgaray - in Washington to lead a delegation that has held talks at the White House - told the Televisa network Mexico's 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."
The executive orders are among a flurry expected on national and border security this week.
Mr Trump is next expected to announce immigration restrictions from seven countries with Muslim-majority populations in the Middle East and Africa. This could affect refugee programmes.
These countries are believed to be Syria, Iraq, Iran, Libya, Sudan, Somalia and Yemen.
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In other developments:
- UK Prime Minister Theresa May will press to renew the UK's special relationship with the US as she prepares to become the first world leader to hold face to face talks with the new president
- Mr Trump said he believed waterboarding - widely considered a form of torture - works, but that he would rely on the advice of Defence Secretary James Mattis and CIA director Mike Pompeo
- Mr Trump ordered cuts in federal grants to so-called "sanctuary cities" - about 400 generally left-leaning locations nationwide that have enacted policies protecting undocumented immigrants within their boundaries, including preventing officials and law enforcement officers from inquiring about immigrant status