US President Donald Trump has pledged not to bend in his demand for a wall along the southern border with Mexico.
But he said the barrier could be made of steel instead of concrete as a potential compromise with Democrats who refuse to fund it.
Trump's comments came at the start of the third week of a partial government shutdown resulting from the dispute that has left hundreds of thousands of federal workers idled or without pay-cheques.
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Trump threatened again, without providing specifics on where the funding would originate, to declare a national emergency as an alternative way to build the wall, depending on the outcome of talks in the coming days.
Democrats have declined to approve the $US5.6 billion ($A7.9 billion) Trump wants to fulfil a 2016 campaign promise to curb illegal immigration.
Led by new Speaker Nancy Pelosi, Democrats passed a bill in the House of Representatives last week to reopen the government without wall funding.
Pelosi has called a border wall immoral.
"This is a very important battle to win from the standpoint of safety, number one, (and) defining our country and who we are," Trump told reporters at the White House before leaving for the Camp David presidential retreat.
"The barrier, or the wall, can be of steel instead of concrete, if that helps people. It may be better," he said.
The White House painted that offer, which Trump floated previously, as an olive branch.
Vice President Mike Pence led a second round of talks with congressional aides on Sunday about the issue, but Trump said he did not expect those talks to produce results, noting that the principals - himself, Pelosi and Senate Democratic leader Chuck Schumer - were the ones who could solve it quickly.
"If we don't find a solution, it's going to go on for a long time. There's not going to be any bend right here," Trump said.
Large chunks of the federal government were shut down on December 22 after lawmakers and the president hit an impasse over Trump's demand that a bill to keep the federal government operational include money to help build a $US23 billion wall along the US border with Mexico.
About 800,000 government workers are either furloughed or working without pay.
"I can relate," Trump, a former New York businessman, said when asked if he could relate to the pain of federal workers struggling to pay their bills.
"I'm sure that the people that are on the receiving end will make adjustments."
Not all Republicans agree with Trump's insistence on keeping government agencies shuttered until the border debate is resolved.
"It is not a sign of weakness to try to figure out a middle ground, and I think that both sides need to indicate a willingness to listen and to compromise," US Senator Susan Collins of Maine said on NBC.
She called the debate over using steel versus concrete "bizarre."