Mexico's President Enrique Pena Nieto cancelled on Thursday a scheduled meeting with US President Donald Trump next week amid a deepening dispute over a border wall promised by America's new leader.

"This morning we informed the White House that I will not attend the work meeting planned for next Tuesday with the POTUS [president of the US]," Pena Nieto said on Twitter. "Mexico reiterates its willingness to work with the United States to reach accords that favour both nations."

The Mexican president's rejection came after Trump said it was "better to cancel" the scheduled visit to Washington if Mexico was unwilling to foot the bill for a border wall.

READ MORE: Trump to Mexico leader - 'Pay for wall or stay away'

There was much debate over who would pay for the costly wall.

Trump said throughout his campaign that he would force Mexico to pay, a proposal Mexico has repeatedly rejected.

The White House said on Thursday that Trump wants a new 20 percent tax on imports from Mexico to pay for the barrier on the southern border.

Trump wants the measure to be part of a broader tax overhaul package that the US Congress is contemplating, White House spokesman Sean Spicer told reporters.

Explaining how the tax would work, Spicer said: "We have a new tax at $50bn at 20 percent of imports - which is, by the way, a practice that 160 other countries do right now."

"Our country's policy is to tax exports and let imports flow freely in, which is ridiculous. But by doing it that way we can do $10bn a year and easily pay for the wall. Just through that mechanism alone," Spicer said.

No further details were available.

Manuel Suarez-Mier, a columnist for Mexico's Excelsior newspaper, told Al Jazeera from Washington, DC, that Trump's ultimatum came as a surprise for the Mexican government.

"The minister of foreign affairs and the minister of commerce were in Washington from Mexico on Wednesday and Thursday to determine the details for the upcoming meeting of the presidents on Tuesday. And Trump comes out and announces that the wall will be built and Mexico will have to pay for it," said Suarez-Mier.

He said that the wall is "totally unnecessary".

"One third of the border is already fenced, another third has a vigorous river dividing the two countries, and the last part if full of mountains and deserts, so it is a very difficult terrain," said Suarez-Mier.

No intention of paying

Pena Nieto has repeatedly condemned Trump's move to build a border wall, and insisted that his country has no intention of paying for it.

"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," Pena Nieto said in a brief televised message on Wednesday.

"Mexico does not believe in walls. I have said it time and again: Mexico will not pay for any wall," he said, referring to Trump's vow to make his southern neighbour pay for the barrier.

Trump's plan has also been roundly condemned by other Latin American leaders .

INFOGRAPHIC: Building Trump's border wall

"Mexico gives and demands respect as the completely sovereign nation that we are," Pena Nieto said.

He said he would wait for a report from a high-level Mexican delegation holding meetings in the US capital this week and consult governors and MPs before deciding on "the next steps to take."

Pena Nieto said he had ordered Mexico's 50 consulates in the US to act as legal counsel for the rights of Mexican migrants.

"Our communities are not alone. The government of Mexico will offer legal counsel that will guarantee the protection they need," he said.

On Wednesday, Trump signed directives to order the building of the wall, and a crackdown on US cities that shield undocumented immigrants.

"A nation without borders is not a nation. Starting today, the US gets back control of its borders," Trump said in an address at the Homeland Security Department.