Mexican President Enrique Pena Nieto has cancelled a meeting with US President Donald Trump following an announcement that construction will soon begin on a wall on the US southern border.

Pena Nieto has long made it clear his country has no intention of funding Trump's proposed wall, and appeared to cancel the meeting in response to a difference of opinion on discussions over payment.

"This morning we informed the White House that I will not attended the work meeting planned for next Tuesday with @POTUS," the Mexican president tweeted on Thursday (26 January).

He also commented on Wednesday that he had no intention of paying for Trump's wall – a message he has reiterated consistently since Trump's presidential campaign.

"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," President Pena Nieto said. "Mexico does not believe in walls. I have said it time and again: Mexico will not pay for any wall."

However, Trump has since claimed the pair reached a mutual agreement to cancel the meeting, The Hill reported.

Speaking at the GOP retreat in Philadelphia, Trump said: "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."

Pena Nieto's latest tweet came shortly after a threat by Trump that he would cancel the meeting if Pena Nieto was not prepared to discuss payment of the wall.

In a series of tweets, Trump wrote: "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. If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting."

On Wednesday Trump signed an executive order giving the wall the go-ahead, and suggested the money would initially come from US taxpayers, with Mexico later reimbursing America for construction – although Trump provided no clear details as to how the payments would be made.

In his speech at the Department of Homeland Security, Trump suggested the wall would also benefit Mexico, stating: "We are in the middle of a crisis on our southern border.

"The unprecedented surge of illegal migrants from Central America is harming both Mexico and the US and I believe the steps we will take starting right now will improve the safety in both of our countries. It's going to be very, very good for Mexico."

However, given Pena Nieto's repeated insistence he will not be paying for a wall, Trump will have his work cut out for him if he wishes to avoid footing the bill for final payment of the wall.