Mexico's President Enrique Pena Nieto hit back at Donald Trump's order to start building a wall separating the country from the United States - and vowed that Mexicans would not foot the bill, despite what Trump has said.

'Mexico does not believe in walls. I've said it time and time again: Mexico will not pay for any wall,' Pena Nieto said in a video published Wednesday evening. The Mexican president said he regrets and rejects the US decision to build a wall.

Meanwhile Trump insisted in an ABC News interview Wednesday that Mexico would 'absolutely' pay for the wall, but failed to clearly explain how that would happen.

Pena Nieto said in his video statement Wednesday that he had asked his government to strengthen protection for Mexican immigrants.

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Mexico's President Enrique Pena Nieto (pictured) hit back Wednesday at Donald Trump's order to start building a wall separating the country from the United States

'I've asked for the minister of Foreign Relations to re-enforce protection measures to our citizens,' he said.

The 50 Mexican Consulates in the US will serve to defend the rights of immigrants, Pena Nieto added.

'Mexico offers and demands respect like the fully sovereign nation we are,' he said. 'Mexico gives its friendship to the people of the United States and wishes to reach agreements with its government - agreements that will be in favor of Mexico and Mexicans.'

Trump meanwhile tried to detail its plan to have Mexico pay for the wall on the border in an ABC News interview, but did not offer a substantiated explanation.

Trump insisted in an ABC News interview Wednesday (pictured) that Mexico would 'absolutely' pay for the wall, but failed to clearly explain how that would happen

TRUMP'S TWO EXECUTIVE ORDERS Donald Trump signed two executive orders on Wednesday. Both are part of his battle against illegal immigration. With one of the decisions, the president ordered work to begin on planning and building a wall on the Mexican border. The US leader instructed officials to begin to 'plan, design and construct a physical wall along the southern border' and see how it could be funded. 'A nation without borders is not a nation,' Trump said, echoing former president Ronald Reagan. In the order, Trump envisions the 'immediate construction of a physical wall on the southern border, monitored and supported by adequate personnel so as to prevent illegal immigration, drug and human trafficking, and acts of terrorism'. Trump has promised to make Mexico pay for the wall, something the Mexican government has repeatedly said it will not do. The US president failed to clearly explain Wednesday how he intends to get Mexico to pay for the wall. 'All it is, is we'll be reimbursed at a later date from whatever transaction we make from Mexico,' he said. Meanwhile Mexican President Enrique Pena Nieto said: 'Mexico does not believe in walls. I've said it time and time again: Mexico will not pay for any wall.' The other executive order signed by the president Wednesday aims at preventing sanctuary cities across the country from offering protection to undocumented immigrants. The order strips sanctuary cities from federal funding. 'The Attorney General and the Secretary, in their discretion and to the extent consistent with law, shall ensure that jurisdictions that willfully refuse to comply with 8 U.S.C. 1373 (sanctuary jurisdictions) are not eligible to receive Federal grants, except as deemed necessary for law enforcement purposes by the Attorney General or the Secretary,' the order reads. 'The Secretary has the authority to designate, in his discretion and to the extent consistent with law, a jurisdiction as a sanctuary jurisdiction.' Trump also gave officials authority to hire 10,000 additional immigration officers. Sources: AFP and Associated Press Advertisement

'All it is, is we'll be reimbursed at a later date from whatever transaction we make from Mexico,' he said.

Pena Nieto was said earlier that day to be 'considering' canceling next week's visit to Washington following Trump's order to begin construction of a wall between Mexico and the US, according to a senior official.

The decision to rethink the visit came amid growing outrage in Mexico, and a sense among many that Pena Nieto has been too weak in the face of Trump's tough policy stance.

The official, who was not authorized to discuss the matter publicly and spoke on condition of anonymity, told The Associated Press the administration 'is considering' scrapping the January 31 visit. 'That's what I can tell you.'

It was not clear when a final decision may be made.

Trump's order came the same day Mexico's foreign relations and economy secretaries arrived in Washington for talks with his administration, and its timing was seen by many in Mexico as a slap in the face.

But Mexican diplomats now see the visit as a chance to improve relations between the two countries

'There is ... frustration with our government and ourselves that we have not been able to tell the story of this important relationship,' a Mexican diplomat told CNN.

'There are a lot of stereotypes of Mexicans in the US, but there are also stereotypes of Americans in Mexico. It is in the interest of both governments to explain what this relationship is and what we can do together.'

Who's paying for the wall? Trump said Mexico is 'absolutely' going to pick up the bill but didn't explain how he intends to make the country comply. One section of fence is pictured near Ciudad Juarez in Mexico

Critics of Pena Nieto - whose approval ratings were just 12 per cent in a recent survey, the lowest for any Mexican president in the polling era - have hammered him for his perceived weakness on Trump. Opposition politicians urged him Wednesday to call off the trip.

'The position is very clear,' said Ricardo Anaya Cortes, president of the conservative opposition National Action Party.

'Either one cancels the meeting with Donald Trump, or one attends it to say publicly and with absolute firmness that Mexico rejects the wall and we will not pay a single cent for it.'

Trump has vowed to force Mexico to pay for the wall, and also to renegotiate the North American Free Trade Agreement. Pena Nieto and other officials have repeatedly said Mexico will not pay.

The US president has also promised to step up deportations. He launched his campaign with remarks calling immigrants crossing in illegally from Mexico criminals, drug dealers and 'rapists'.

Close that door: Pena Nieto was said earlier that day to be 'considering' canceling next week's visit to Washington following Trump's order to begin construction of a wall between Mexico and the US (pictured in El Paso)

Trump added that 'some' were presumably good people, but the comments nonetheless deeply offended many Mexicans.

Pena Nieto was roundly criticized after inviting then-candidate Trump to Mexico City last August and disappointed many of his countrymen by not publicly confronting Trump on the wall.

On Tuesday, ahead of their trip to Washington, the economy and foreign relations secretaries suggested that Mexico could leave NAFTA if negotiations with Washington are unsatisfactory — though that would not be the first choice.