US Vice-President Mike Pence says the White House is looking into the legality of declaring a national emergency to circumvent Congress and begin construction of President Donald Trump's long-promised border wall.

Key points: Mr Trump will make a national address before making his first visit to the wall since March

Mr Trump will make a national address before making his first visit to the wall since March New House Speaker Nancy Pelosi says building a wall is "immoral"

New House Speaker Nancy Pelosi says building a wall is "immoral" Pressure to end the shutdown is likely to build amid possible cuts in food stamp programs and delayed tax refunds

He said Mr Trump continued to weigh the idea but had yet to make a decision on the 17th day of the partial government shutdown over funding for the wall.

The comments come as the President prepares to deliver a prime-time address to the nation on immigration and visit the US-Mexico border this week.

Mr Pence briefed reporters alongside Homeland Security Secretary Kirstjen Nielsen and other senior administration officials.

He said the President had invited Democratic leaders Chuck Schumer and Nancy Pelosi, who says building a wall is "immoral", back to the White House to continue their discussions.

But he said Mr Trump was not budging on his demand for billions of dollars for the wall, which the President says is necessary to stem illegal immigration.

Trump to make prime-time national address

White House spokeswoman Sarah Sanders announced on Twitter that Mr Trump would make a trip to the border on Thursday (local time) and said details would be released soon.

The visit will likely highlight security concerns pushed by the administration as justification for the wall.

A short while later, Mr Trump said in his own Twitter post that he would address the nation at 9:00pm on Tuesday night (1:00pm AEDT on Wednesday) on the border situation.

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Politicians and Mr Trump hit an impasse last month over his demand that a bill to keep the federal government operational include money for a wall along the border with Mexico.

About 800,000 government workers are either on leave or working without pay.

Mr Trump said in December he would be "proud" to shut the government down over the wall and last week told politicians it could last months.

Sorry, this video has expired Donald Trump says he's prepared to accept a steel wall

However, pressure to reach a deal is likely to grow as the effects of the shutdown are felt, including possible cuts in food stamp programs and delayed tax refunds.

Mr Trump skipped a planned trip to Florida to stay in Washington during the Christmas and New Year's holidays after large chunks of the federal government were shut on December 22.

He exhorted Democrats in Congress to "come back from vacation" and approve funding for his wall.

Democrats returned to Washington in the new year, taking control of the US House of Representatives, and passed legislation to reopen all closed government agencies but did not include wall funding.

This week, they will pass a series of bills to reopen federal agencies after weekend talks between the Trump administration and Democratic negotiators failed to end a stalemate.

On Sunday, Mr Trump pledged not to bend in his demand for $US5.6 billion ($7.8 billion) to pay for the wall but said the barrier could be made of steel instead of concrete as a potential compromise with Democrats who refuse to fund it.

Mr Trump has argued the wall is necessary for national security and has tried to link terrorism to illegal immigration, without providing evidence, as justification for the plan.

Democrats say the wall is expensive and inefficient, as well as contrary to American values.

Mr Pence also said he and Ms Nielsen would be visiting the Capitol on Tuesday and Wednesday to brief House and Senate members.

Mr Trump visited the southern border last March.

Reuters