MEXICO CITY (AFP) - Criticism rained down on President Enrique Pena Nieto Wednesday (Aug 31) as indignant Mexicans asked why he invited Donald Trump, of all people, to visit.

The Republican presidential candidate, who forged his campaign with insults against Mexican immigrants, surprised everyone on Tuesday by taking up Pena Nieto's invitation.

He was expected on Wednesday in Mexico City where a storm of protests was already under way.

"There is no explanation for a private meeting between the president and a candidate who has consistently offended Mexico and above all its people," said Jesus Zambrano, the president of the lower house of the Mexican Congress.

He said it was a "dubious way" of defending Mexico's interests.

The meeting was expected to begin at around 2pm (3am on Thursday, Singapore time) at Los Pinos, the presidential residence.

"I believe in dialogue to promote the interests of Mexico in the world and mainly to protect Mexicans wherever they are," Pena Nieto said on Twitter late on Tuesday, explaining why he invited both Trump and his Democratic rival Hillary Clinton to meet with him.

Former foreign minister Jorge Castaneda said, however, "without a public apology by Trump for the things he has said, he should not be welcomed in Mexico nor at Los Pinos, especially since he's not a head of state."

Margarita Zavala, the wife of former president Felipe Calderon and a possible presidential candidate for the conservative National Action Party, wrote an open letter to Trump.

"Although you have been invited, know that you are not welcome. The Mexican people have dignity and we reject your hate speech," she wrote.

Trump launched his presidential campaign with attacks on immigrants from Mexico as drug traffickers and "rapists." His vow to build a great wall on the southern US border and make Mexico pay for it is the signature pledge of his campaign.

After meeting with Pena Nieto, Trump plans to make a major speech in Arizona, a US border state, on illegal immigration later on Wednesday.

What the Mexican President gains from meeting Trump, whom he once compared to Hitler and Mussolini, is a puzzle to many here.

Five years into a six-year term, Pena Nieto is already deeply unpopular, with his approval ratings down to 23 per cent.

"I think that President Pena Nieto is taking an enormous political risk by hosting Trump," said former president Vicente Fox on CNN.

"If he's gone soft on Trump, it will hurt him greatly. He will even be considered like a traitor because we don't accept to be offended."

The leftist Party of the Democratic Revolution (PRD) said the meeting "only favours the political aspirations of this demagogue."

Castaneda said it would only make sense if Trump apologised and announced in Arizona that he would no longer insist on building a border wall.