Mexico's President Enrique Pena Nieto and Donald Trump have agreed not to talk publicly for now about payment of the border wall the US President wants to build.

The pair had a "constructive and productive" phone call and broached issues including the US trade deficit with Mexico and the flow of illegal arms and drugs across the border, the Mexican Government said.

"Regarding payment of the border wall, both Presidents recognised their clear and very public differences of opinion on this sensitive subject, and agreed to resolve their differences as part of a comprehensive discussion on all aspects of the bilateral relationship," a statement by Mexico said.

Mr Trump said the conversation was friendly but he will renegotiate trade deals and other aspects of the countries' ties because Mexico has "beat us to a pulp" in the past.

"We had a very good call. I have been very strong on Mexico. I have great respect for Mexico," Mr Trump said.

"But, as you know...they've made us look foolish."

The two men spoke for about an hour, a day after Mr Pena Nieto scrapped a planned meeting in Washington next week over Mr Trump's instance that Mexico pay for the wall.

"We are going to be working on a fair relationship and a new relationship" with Mexico, Mr Trump said.

"But the United States cannot continue to lose vast amounts of business, vast amounts of companies and millions and millions of people losing their jobs.

"That won't happen with me."

The Republican President views the wall, a major promise during his election campaign, as part of a package of measures to curb illegal immigration.

Mexico has long insisted it will not heed Mr Trump's demands to pay for the construction project.

On Thursday, White House spokesman Sean Spicer sent the Mexican peso falling to its low for the day when he told reporters Mr Trump wanted a 20 per cent tax on Mexican imports to pay for the wall.

Mr Spicer gave few details, but his comments resembled an existing idea, known as a border adjustment tax, that the Republican-led US House of Representatives is considering as part of a broad tax overhaul.

Mexico and the US will be stuck at an impasse unless they solve Mr Trump's "unacceptable" demand of payment for the border wall, Mexico's Economy Minister Ildefonso Guajardo said.

Reuters/ABC