US President Donald Trump is ramping up his efforts to make a public case for his border wall as the partial government shutdown is now in its third week, planning a prime-time address tomorrow and a visit to the border on Friday.

Trump announced the news of his presidential address in a tweet.

"I am pleased to inform you that I will Address the Nation on the Humanitarian and National Security crisis on our Southern Border," he said.

The President insists that any funding bill to reopen federal agencies include US$5.7 billion for his border wall.

Trump made his first visit to the border as president 10 months ago. During that trip, Trump toured 9m-tall steel and concrete prototypes of the border wall in California and strongly condemned jurisdictions that offer "sanctuary" to undocumented immigrants.

Trump and congressional Democrats remain at an impasse on crafting a deal to reopen the government, which is in its 17th day of a partial shutdown.

Democrats, who retook control of the House last week, have passed measures that would fund the federal agencies affected, but Trump has balked at any legislation that does not meet his demand for border wall funding. Talks over the weekend showed no signs of a breakthrough, and hundreds of thousands of federal workers remain at home.

Trump said that he understood the predicament facing federal workers who are not receiving their pay.

"I can relate, and I'm sure the people who are on the receiving end will make adjustments; they always do," Trump told reporters outside the White House. He also claimed that "many of those people agree with what I'm doing": refusing to reopen the government without obtaining funding for the wall, one of his signature campaign promises.

With the impact of the partial shutdown rippling across the country, acting White House budget director Russell Vought sent a letter to congressional leaders detailing the Administration's demands.

The letter called for US$5.7 billion "for construction of a steel barrier for the Southwest border" but also proposed "an additional US$800 million to address urgent humanitarian needs" and unaccompanied migrant children arriving at the border.

In a tweet, Trump sought to put a positive spin on the ongoing negotiations, describing them as "productive" and declaring that "we are now planning a Steel Barrier rather than concrete".

But a Democratic official said no progress was made over the weekend, in large part because the White House has not been forthcoming about how the money would be used or why the request is for so much more than the Administration sought only a few months ago.

Trump has said in recent days that he might seek to unilaterally secure border wall funding by declaring a national emergency, a move that experts say would be of questionable legality.

House Speaker Nancy Pelosi sharply criticised Trump for raising that possibility, suggesting in an interview with CBS News that the President "would like to not only close government, build a wall, but also abolish Congress so the only voice that mattered was his own".