President Donald Trump has signed directives to begin building a wall along US border with Mexico and crack down on US cities that shield undocumented immigrants, moving quickly on sweeping and divisive plans to curb immigration and boost national security.

The move "will improve safety in both countries", Trump said after signing the orders on Wednesday.

"A nation without borders is not a nation. Starting today, the US gets back control of its borders," he said.

"This will help dismantle cartels, keeping illegal weapons and cash from flowing out of American and into Mexico."

The order, signed on Wednesday, will enable construction of "a large physical barrier on the southern border", spokesman Sean Spicer said.

"Building this barrier is more than just a campaign promise, it's a common sense first step to really securing our porous border," Spicer added.

"This will stem the flow of drugs, crime, illegal immigration into the United States."

The measure will also bolster resources for border security agents, increase detention space for undocumented immigrants and ensure people are deported.

In an interview with ABC News on Wednesday, Trump said construction of the wall would start within months, with planning starting immediately, and that Mexico would pay back to the US "100 percent" of the costs.

READ MORE: Latin America leaders condemn Trump's Mexico wall at CELAC summit

"We'll be reimbursed at a later date from whatever transaction we make from Mexico," Trump said.

"I'm just telling you there will be a payment. It will be in a form, perhaps a complicated form. What I'm doing is good for the United States. It's also going to be good for Mexico. We want to have a very stable, very solid Mexico."

Condemning the move, Mexican President Enrique Pena Nieto said his country will not pay for the construction of the wall.

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

"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," Pena Nieto said in a brief televised message.

The Mexican leader did not comment on his forthcoming trip to the US to meet Trump.

Reuters news agency reported that the Republican president is expected to take steps in the coming days to limit legal immigration, including executive orders restricting refugees and blocking the issuing of visas to people from several Muslim-majority Middle Eastern and North African countries including Syria, Sudan, Somalia, Iraq, Iran, Libya and Yemen.

The second executive order, signed during an appearance at the Department of Homeland Security, was to strip federal grant money from "sanctuary" states and cities, often governed by Democrats, that harbour illegal immigrants.

In an interview with ABC news network, the US president clarified that "illegal immigrants brought to US as children shouldn't be very worried".