The US government partial shutdown was set to stretch deep into next week after legislators failed Thursday to make a breakthrough in the row over President Donald Trump's demand for a US-Mexico border wall.

After convening for just a few minutes following the official Christmas break, a still nearly empty Senate adjourned, deciding to renew budget deliberations only next Wednesday, the last day of the current Republican-controlled Congress.

That would take the government shutdown, already on its sixth day, into 12.

Both sides have dug in, with Democrats refusing to provide $5 billion for Trump's border wall project and the president insisting he will not fully fund the government unless he gets the money.

White House spokeswoman Sarah Sanders accused Democrats of "openly choosing to keep our government closed to protect illegal immigrants rather than the American people."