US President Donald Trump has said that if the government shutdown stalemate continued, Republicans should fund the government by changing Senate rules, which currently require a super-majority for appropriations bills to pass.

In a tweet, Mr Trump warned of taking the "nuclear option" in relation to tackling the shutdown.

"The Dems (Democrats) just want illegal immigrants to pour into our nation unchecked. If stalemate continues, Republicans should go to 51 percent (Nuclear Option) and vote on real, long term budget," Trump said on Twitter.

Mr Trump's proposal was almost immediately rejected by a spokesman for Senate Republican Leader Mitch McConnell.

The spokesman said that Senate Republicans oppose changing the chamber's rules so that legislation to fund the government and end the current shutdown could pass with a simple majority.

"The Republican Conference opposes changing the rules on legislation," the spokesman said.

Current Senate rules require a super-majority of three-fifths of the chamber, usually 60 out of 100, for legislation to clear procedural hurdles and pass.

Funding for federal agencies ran yesterday with Mr Trump and Republicans locked in a standoff with Democrats.

There appeared to be no clear path for a quick end to the crisis.

Democrats say short-term spending legislation must include protections for illegal immigrants brought to the United States as children, known as "Dreamers."

Republicans, who have a slim 51-49 Senate majority, said they would not negotiate on immigration until the government was reopened.