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

The Republican president is also 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.

Mr Trump signed two executive orders during an appearance at the Department of Homeland Security, one on building a wall along the roughly 3,200km US-Mexico border and the other to strip federal grant money from "sanctuary" states and cities, often governed by Democrats, that harbor illegal immigrants.

In cities such as San Francisco local officials, often Democrats, refuse to cooperate with federal authorities on actions against illegal immigrants. 

"The American people are no longer going to have to be forced to subsidise this disregard for our laws," White House spokesman Sean Spicer said.

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

During a White House briefing, Mr Spicer referred to the wall as "a large physical barrier on the southern border."

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

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

Mr Trump has long said that he will make Mexico pay for the wall. 

"We'll be reimbursed at a later date from whatever transaction we make from Mexico," he told ABC.

"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." 

US House of Representatives Speaker Paul Ryan said tonight the House would fund the wall.

"We're going to pay for it and front the money up," Mr Ryan said in an interview with MSNBC when asked who is going to pay for the wall.

"There are a lot of different ways of getting Mexico to contribute to doing this," Mr Ryan said.

Many Democrats have opposed the plan and could try to thwart any legislation to pay for the construction in the US Congress, although Republicans control both the Senate and House of Representatives.

Mr Trump's plans prompted an immediate outcry from immigrant advocates who said he was jeopardising the rights and freedoms of millions of people.

"The border wall is about political theatre at the expense of civil liberties," said Christian Ramirez, director of the Southern Border Communities Coalition immigrant advocacy group. 

"It is not national security policy. Border communities are among the safest in the nation and patrolling them with tens of thousands of heavily armed, poorly trained, unaccountable agents puts lives at risks. This will turn these communities into defacto military zones," Mr Ramirez said. 

Mr Trump made cracking down on illegal immigration a key element of his presidential campaign, with supporters often chanting "Build the wall," during his rallies.

The cost, nature and extent of the wall remain unclear.

Mr Trump last year put the cost at "probably $8 billion," although other estimates are higher, and said the wall would span 1,600km because of the terrain of the border.

Mr Spicer said Mr Trump's directives would also end the practice known by critics as "catch and release" in which authorities apprehend illegal immigrants on US territory but do not immediately detain or deport them.

He said they would create more detention space for illegal immigrants along the southern border to make it easier and cheaper to detain and deport them.

Mr Trump's actions could fundamentally change the American stance on immigration, as well as further testing relations with Mexico.

Many Americans view their country with pride as "a nation of immigrants," and President John Kennedy wrote a book with that title more than half a century ago. But Mr Trump successfully tapped into resentment toward the roughly 11 million illegal immigrants already in the United States and said during the campaign he would deport them all.

Mr Trump, who in announcing his presidential bid in June 2015 accused Mexico of sending rapists and criminals into the United States, has also threatened to slap hefty taxes on companies that produce in Mexico for the US market and to tear up the North American Free Trade Agreement (NAFTA) between Mexico, Canada and the United States.

Mr Trump and Mexican President Enrique Peña Nieto are due to meet next week.

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Earlier today, Mr Trump tweeted that he will seek a "major investigation" on voter fraud, which will focus on two states and illegal voters.

He said that the investigation will look at "those who are illegal and ... even, those registered to vote who are dead".

He said the result of the investigation will determine if "we will strengthen up voting procedures!"

Mr Trump and the White House have failed to provide any evidence for the president's repeated claims that several million people voted illegally in the November poll that brought him to power.