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Donald Trump has hit out at Mexico after its president cancelled next week's visit to the White House.
The US president said meeting Enrique Pena Nieto would be "fruitless" if Mexico didn't treat the US "with respect" and pay for a new border wall.
The diplomatic spat comes a day after Mr Trump unveiled his plan to build a barrier along the Mexico-US border.
Senate Republicans said the US Congress would move ahead with the plan, and it would cost $12bn (£9.5bn) to $15bn.
Mr Trump told Republican lawmakers in Philadelphia that the two leaders had mutually agreed to cancel the summit, adding, "the American people will not pay for the wall."
"Unless Mexico is going to treat the United States fairly, with respect, such a meeting would be fruitless, and I want to go a different route. We have no choice."
White House spokesman Sean Spicer told reporters they were looking "for a date to reschedule", adding they will "continue to keep the lines of communication open".
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Media caption"US to begin building wall immediately" Mr Pena Nieto announced earlier on Thursday he had called off the 31 January trip after Mr Trump suggested he should do just that.
"If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting," the US president wrote on Twitter on Thursday morning.
In a televised address, Mr Pena Nieto said he "lamented" the plans for the barrier.
The Mexican leader 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."
Mr Pena Nieto met Mr Trump - then a presidential candidate - in Mexico City in September and came under intense criticism at home. His approval ratings remain low.
Nieto had no option - Will Grant, BBC News, Mexico City
Mr Nieto is facing the lowest approval ratings of any Mexican president over the past two decades. Much of that unpopularity is down to Donald Trump. Many Mexicans consider their leader lacks the necessary steel to deal with the new Republican president and has been railroaded on everything from the border wall to Nafta.
So when President Trump challenged - some might even say goaded - him to cancel their meeting, Mr Pena Nieto was left with little other option.
He would have been perceived as very weak if he had travelled to Washington for talks and for many here, it would have been tantamount to accepting Mr Trump's central claim - that Mexico will pay for the US border wall. If not up front, then eventually.
That is simply unacceptable to most ordinary Mexicans who view the wall as unnecessary, inhumane, expensive and ineffective.
As their elected leader, at least for the next 18 months, Enrique Pena Nieto was duty-bound to deliver that message to the White House.
On Thursday, US media reported the chief of US Border Patrol is leaving his job.
It is unclear if Mark Morgan, who heads the agency charged with securing US borders, was forced out or resigned.
Building a barrier along the 2,000 mile (3,200km) US boundary with Mexico was one of Mr Trump's key election pledges.
Mexicans were also outraged when Mr Trump described their migrants as murderers and rapists, while launching his campaign in 2015.
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The US president said meeting Enrique Pena Nieto would be "fruitless" if Mexico didn't treat the US "with respect" and pay for a new border wall.
The diplomatic spat comes a day after Mr Trump unveiled his plan to build a barrier along the Mexico-US border.
Senate Republicans said the US Congress would move ahead with the plan, and it would cost $12bn (£9.5bn) to $15bn.
Mr Trump told Republican lawmakers in Philadelphia that the two leaders had mutually agreed to cancel the summit, adding, "the American people will not pay for the wall."
"Unless Mexico is going to treat the United States fairly, with respect, such a meeting would be fruitless, and I want to go a different route. We have no choice."
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White House spokesman Sean Spicer told reporters they were looking "for a date to reschedule", adding they will "continue to keep the lines of communication open".
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Media caption"US to begin building wall immediately" Mr Pena Nieto announced earlier on Thursday he had called off the 31 January trip after Mr Trump suggested he should do just that.
"If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting," the US president wrote on Twitter on Thursday morning.
In a televised address, Mr Pena Nieto said he "lamented" the plans for the barrier.
The Mexican leader 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."
Mr Pena Nieto met Mr Trump - then a presidential candidate - in Mexico City in September and came under intense criticism at home. His approval ratings remain low.
Nieto had no option - Will Grant, BBC News, Mexico City
Mr Nieto is facing the lowest approval ratings of any Mexican president over the past two decades. Much of that unpopularity is down to Donald Trump. Many Mexicans consider their leader lacks the necessary steel to deal with the new Republican president and has been railroaded on everything from the border wall to Nafta.
So when President Trump challenged - some might even say goaded - him to cancel their meeting, Mr Pena Nieto was left with little other option.
He would have been perceived as very weak if he had travelled to Washington for talks and for many here, it would have been tantamount to accepting Mr Trump's central claim - that Mexico will pay for the US border wall. If not up front, then eventually.
That is simply unacceptable to most ordinary Mexicans who view the wall as unnecessary, inhumane, expensive and ineffective.
As their elected leader, at least for the next 18 months, Enrique Pena Nieto was duty-bound to deliver that message to the White House.
On Thursday, US media reported the chief of US Border Patrol is leaving his job.
It is unclear if Mark Morgan, who heads the agency charged with securing US borders, was forced out or resigned.
Building a barrier along the 2,000 mile (3,200km) US boundary with Mexico was one of Mr Trump's key election pledges.
Mexicans were also outraged when Mr Trump described their migrants as murderers and rapists, while launching his campaign in 2015.
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