British officials want the row resolved in time for the 25th anniversary of peace in Northern Ireland. It would also pave the way for a state visit by the US President to mark the milestone. Brussels has taken a hardline approach to imposing the customs rules agreed in the Brexit deal, which has inflamed tensions in the region.
The Northern Ireland Executive remains suspended after the Democratic Unionist Party walked out over the new border checks.
Tensions over the protocol have spilled over into relations between the US and UK with a trade deal now on the backburner.
But President Biden insisted the UK is “our closest ally in the world” at the start of the talks with Ms Truss.
“I look forward to working closely with you. You’re our closest ally in the world and there’s a lot we can continue to do together,” he said.
“We are both committed to protecting the Good Friday Agreement of Northern Ireland, and I’m looking forward to hearing what’s on your mind.”
Ms Truss said she was keen to make progress on ending the deadlock.
US national security adviser Jake Sullivan said the protocol would be discussed “in some detail” with Ms Truss.
He said the president “will encourage the UK and the European Union to work out an effective outcome that ensures there is no threat to the fundamental principles” of the peace process.
Diplomats say the 25th anniversary of the Good Friday Agreement next April would be an obvious time for Mr Biden to visit the UK if the stalemate is resolved.
One senior diplomatic source said: “If you look at the calendar you will conclude that next year might be an obvious reason to visit Europe if things come good.”
A visit by President Biden may not technically be classed as a state visit if Charles III is still yet to be crowned by then.
But it would be a state visit in all but name, with the president meeting the new King in a formal setting.
Mr Biden, who has Irish heritage, has repeatedly intervened to warn the UK against ripping up the Brexit rules.
But diplomats insisted that behind the scenes the UK has a valid argument about the way some trade rules are being imposed.
Americans want allied unity on every issue possible while the West battles Russian aggression, the insider said.
They want to see a “negotiated outcome” between the EU and the UK.
“They believe that we have a good point on some of the trading issues, the goods actually getting to the shelves, and they are prepared to tell the EU that.
“But they continue to urge both sides to go for a negotiated settlement.”
Sir Tony Blair has been working behind the scenes to find ways to resolve tensions and has been “explaining why the EU proposals will not work”.
“He doesn’t agree with the government on every point, but he certainly has been a helpful voice in that,” the source said.
A spokesman for Sir Tony declined to comment.
Ms Truss, who met President Biden before becoming Prime Minister, had hoped to make a visit to the White House this week but the trip to the US was curtailed following the death of the Queen.
Officials are now advising her to wait until after the mid-term elections in the US before making a formal visit to Washington.
Dame Karen Pierce, Britain’s ambassador to the United States, said the “special relationship” between the UK and US is as “strong as it ever has been”.
She said President Biden and Ms Truss, will get on well, they’re both good politicians”.
“Both of them are optimistic about the future. Both of them are good problem solvers,” she added.
“I think the president and the Americans have some understanding that trade disruption is not helpful in the context of bringing communities together.”
Mr Biden and Ms Truss were meeting after the president sent a tweet just as the PM was discussing her economic policy, which said he was “sick and tired of trickle-down economics”.
“It has never worked,” he said.
The comments underlined the differences between the two leaders’ stances just as Ms Truss says she wants to foster closer ties with international allies.
The Prime Minister’s official spokesman said it was “ludicrous” to suggest Mr Biden was criticising UK policy, arguing each country is facing different economic challenges.