Giving no ground on his demand for $US5.7 billion to fund a US-Mexico border barrier as part of any bill to fully reopen the government, Trump's package sought to pile pressure on Democrats by appealing to immigrants they have tried to help.

In a speech from the White House, Trump offered three years of protections for the young undocumented immigrants known as "Dreamers," as well as holders of temporary protected status (TPS), another class of immigrants to the US.

Decrying what he called a "badly broken" US immigration system, Trump said, "I am here today to break the logjam and provide Congress with a path forward to end the government shutdown and solve the crisis along the southern border."

But the protections he proposed fell far short of the path to citizenship for Dreamers that Democrats and some Republicans in Congress have been urging for years.

In a statement after Trump's speech, Senate Republican Leader Mitch McConnell called the president's plan a "bold solution to reopen the government, secure the border, and take bipartisan steps toward addressing current immigration issues."

A spokesman for McConnell said he would seek Senate passage of the president's proposal next week.

Democrats insisted talks on border security occur only after the government is reopened.

"It was the president who singled-handedly took away DACA and TPS protections in the first place. Offering some protections back in exchange for the wall is not a compromise but more hostage taking," Senate Democratic Leader Chuck Schumer said.

Even before Trump spoke, House of Representatives Speaker Nancy Pelosi had said his offer as reported in advance was "unacceptable," did not "represent a good-faith effort to restore certainty to people's lives," and was unlikely to gain the votes needed to pass the House or the Senate.

About a quarter of the US government has been partially shut down since December 22 due to a lack of funding that expired for reasons mostly unrelated to the border or immigration. Some 800,000 federal workers have been staying home on furlough or working without pay.

The president has refused to consider legislation needed to fully reopen the government unless it includes funds that he wants to help pay for a border wall or other barrier, which he says is needed to keep out illegal immigrants and drugs.

The full cost of such a barrier could eventually top $US24 billion, according to some government estimates.

Trump also asked Congress for $US782 million to hire an additional 2,750 border agents, law enforcement officers and staff, and another $US563 million to hire 75 new immigration judge teams to reduce a backlog in immigration courts.

Polls showed Americans increasingly blame Trump for the shutdown, the 19th to occur since the mid-1970s. Most past shutdowns have been brief.

Australian Associated Press