MEXICO CITY - Mexico's President Enrique Pena Nieto and his US counterpart Donald Trump on Friday agreed to keep a bitter and ongoing dispute over a border wall project out of the public realm, the office of the presidency said.

The two "spoke for an hour by telephone," a day after Pena Nieto cancelled a meeting with Trump that was to take place on Tuesday.

Pena Nieto cancelled the visit after Trump tweeted there was no point in meeting if Mexico was not prepared to pay for a wall along the US' southern border.

In a statement, the presidency said, "in regard to paying for the border wall, both presidents acknowledged their clear and very public positions on such a sensitive issue, and agreed to resolve these differences as part of a comprehensive discussion on all aspects of the bilateral relationship."

Both "also agreed to not talk about this controversial matter in public for now."

Pena Nieto and Trump have instructed their teams "to continue to dialogue to strengthen this important strategic and economic relationship in a constructive way," his office added.

The leaders had a "constructive and productive conversation" on bilateral ties, "including the US' trade deficit with Mexico, the importance of the friendship between our two nations, the need for our countries to work together to stop drug trafficking and the illegal flow of arms," the office said.

Surprisingly, no mention was made of illegal immigration from Latin America, especially Mexico, to the US.

Trump has said the wall is needed to keep out illegal migrants, as well as prevent trafficking.

The call was "arranged by their work teams," the office said.