Pena Nieto extended invitations to both candidates last month, and Trump flew to Mexico City last Wednesday for a meeting that appeared to be friendly but later revealed deep tensions.

Nieto has said he was the one who made a decision to invite the two major U.S. presidential candidates.

Pena Nieto also has been ridiculed for not confronting him more directly about comments calling migrants from Mexico criminals, drug-runners and "rapists", and Trump's vows to build a border wall and force Mexico to pay for it.

The new finance minister, Meade, is a friend of Videgaray and had started in the administration as foreign minister before moving to the social development ministry previous year. The 48-year-old, who ran Pena Nieto's election campaign, was widely seen as the president's top aide, with a huge influence on policy.

The president's office announced earlier Wednesday that Pena Nieto would have a message later in the day about a change in his government.

Pena Nieto said Meade will be in charge of turning in a primary budget surplus for next year, meaning government spending will have to be less than revenues, not including interest payments on debt.

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Meanwhile, Trump has pledged to be coming up with a wall on the USA border to help Mexico keep migrants out as well as also to deport millions of undocumented immigrants.

Videgaray, who has also been rumored as a potential 2017 gubernatorial candidate for the ruling party in the State of Mexico, a populous region next to the capital, will not take another public post, the spokeswoman for his ministry said. "It was necessary to make him feel and know why Mexico does not accept his positions".

However, Mr Trump's visit nearly immediately caused public relations problems, when he appeared later that day at a rally in Arizona.

A day later, Mr Trump tweeted that Mexico would pay for the wall, and Mr Pena Nieto fired back his own tweet saying that would "never" happen.

Following Donald Trump's visit to Mexico, Hillary Clinton told ABC Newsthat she won't be traveling to Mexico any time before the November 8 election.