United States President Donald Trump warned of murderers and gangsters spreading across the country during a visit to the US-Mexican border Thursday to push his demand for a multi-billion dollar wall.

Trump used the backdrop of the Rio Grande border river at McAllen, Texas, to ramp up what has already turned into a hugely messy political fight with Democratic opponents, resulting in the shutdown of swaths of the US government.

With typical rhetorical flourishes, Trump said that only building more walls along the Mexican border could stop an onslaught of violent crime.

"They just go where there's no security and you don't even know the difference between Mexico and the United States," he told a meeting of border patrol officers. "They have women tied up, they have tape over their mouths, electrical tape."

"If we had a barrier of any kind, a powerful barrier, whether its steel or concrete ... we would stop it cold," Trump said.

Opposition Democrats are refusing to approve $5.7 billion in wall funding, saying that overwhelming numbers of illegal immigrants do not commit serious crimes and that Trump is mainly promoting the project to satisfy his right-wing base.

Trump said that illegal immigrant crime stretched right up into the north of the country. However, widely respected studies show that illegal immigrants commit fewer crimes than people born in the United States.

Government shutdown goes on

That has resulted in a partial government shutdown now in its 20th day, with hundreds of thousands of federal employees — including air traffic controllers, the FBI and Coast Guard — going without pay.

Signalling he's ready to maintain the game of brinksmanship, Trump tweeted on arrival in Texas that he will scrap a visit to the annual World Economic Forum in Davos, Switzerland, which runs from January 21-25.

Trump had been expected to make a brief appearance at the influential get-together, attended by many world leaders, but said that opposition Democratic "intransigence" required him to stay home.

National emergency?

Trump said he was ready to expand the debate over funding for a border wall to some of the other issues surrounding the over-burdened US immigration system — a suggestion that could open the door to working with Democrats.

"I would like to do a much broader form of immigration," he said in Texas.

But throughout the day, the frustrated president also repeated his threat to declare a national emergency and give himself authority to go around Congress if he can't get approval for the wall.

Speaking to Fox News in an interview broadcast on Thursday evening, Trump reiterated he had "the absolute right to declare a national emergency".

But pressed on a timeline for doing so, he said he would "see what happens" over the coming days.

Analysts say the declaration would likely be challenged in court as a case of presidential overreach, in which case the wall still could face being blocked.

However, it would still give Trump political cover with his base by showing he'd done what he could. At that point, Trump could end the partial government shutdown and declare a win.

White House walkout

Trump, who revels in telling stories about his negotiating skills as a New York real estate magnate, has not managed to get the Democrats to budge on his demand for the $5.7 billion.

On Wednesday, he invited Democrat leaders to the White House, but walked out of the meeting.

"A total waste of time," Trump tweeted. "I said bye-bye, nothing else works!"

Chuck Schumer, the top Democrat in the Senate, told journalists Trump "sort of slammed the table," then "got up and walked out".

"Again, we saw a temper tantrum because he couldn't get his way," Schumer said.

Trump disputed that on Thursday, saying "I didn't pound the table. That is a lie."

"I don't have temper tantrums," he said.

On Thursday, US media reported the White House had asked the Army Corps of Engineers to look into the possibility of diverting funds allocated for relief projects in areas damaged by natural disasters, such as Puerto Rico and Florida.

21 bodies found in Mexico

Few on either side of the debate dispute that the border poses a significant challenge. Illustrating the danger, Mexican authorities said on Thursday they had found 21 bodies after a gang shootout in Miguel Aleman, a town about 270 kilometres across the border from McAllen, Texas.

However, Trump's opponents say he is hyping the danger posed to Americans to stir xenophobia for his own political gains.

Yanira de Hernandez, a 52-year-old Salvadoran migrant who hopes to get to US soil from Mexico, said she simply dreams of a better life in a country built on immigration.

"Everyone has the right to emigrate, to seek a new future. We're not going to commit any crimes. We hope he (Trump) understands that and that God helps him to change, because his ancestors were migrants too," she said in the Mexican border city of Tijuana.