US President Donald Trump announced on Monday he would make a prime-time address and visit the US-Mexico border this week as the partial federal government shutdown entered its 17th day after a funding impasse over his demand for money to build a border wall.

The moves indicate the Republican president has no intention of backing off his pledge to build a wall that he believes will stem irregular immigration and drug trafficking. Democrats in Congress say a wall would be expensive, inefficient and immoral.

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

Vice President Mike Pence said White House lawyers were evaluating the possibility that Trump could declare a national emergency in order to secure alternate funding for the wall but that Trump had not made a decision on using that tactic. It was unclear what basis Trump could use to declare a national emergency, and legal experts expected challenges if Trump were to move forward with the declaration.

Trump planned to visit the US-Mexico border on Thursday, White House Spokeswoman Sarah Sanders announced on Twitter without providing details. The visit likely will highlight security concerns pushed by the administration as justification for the wall.

A short while after Sanders's tweet, Trump tweeted that he will address the nation on Tuesday at 9pm Eastern time (02:00 GMT on Wednesday) to discuss what he called a humanitarian and national security crisis on the southern US border.

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Large chunks of the federal government shut down on December 22 over Trump's demand that a bill to keep the federal government operational include more than $5bn to pay for a wall along the border with Mexico. About 800,000 government workers have been either furloughed or working without pay since the shutdown began.

Trump directed the White House budget office to take steps to mitigate the effects of the shutdown, including ensuring tax refunds are delivered, Pence told reporters.

Pence said Trump also invited Democrats back to the White House to respond to its latest proposal to resolve the standoff over legislation to fund the government.

Pence, who participated in weekend discussions on the shutdown, said Democratic staff said there would be no negotiations until the government is reopened.

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.

Democrats returned to Washington, DC 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.

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On Sunday, Trump pledged not to bend in his demand for money 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.

Democrats say Trump has no grounds to declare a national emergency over the issue.

They also say other border security measures are more efficient and cost-effective than a wall, which they say is contrary to American values.

Trump visited the southern border last March.

Trump has previously given three prime-time televised addresses and two during the day, according to data compiled by CBS News.