Joe Biden has played down the chances of a post-Brexit free trade deal between the US and UK, as he held talks with Boris Johnson at the White House.
The US president said he would discuss the issue "a little bit" with the UK prime minister, adding: "We're going to have to work that through."
Downing Street said a direct deal with the US remained the "priority".
But UK ministers are pondering joining an existing North American trade pact instead, the BBC understands.
Mr Biden and Mr Johnson also discussed Northern Ireland, climate change and Afghanistan during the 90-minute meeting.
The UK is keen to strike free trade deals around the world in the wake of leaving the European Union's single market - including with the US, with which annual trade was worth an estimated $273bn (£200bn) in 2019.
A deal would encourage more business between the two countries by making it cheaper, usually by reducing or eliminating taxes called tariffs.
But Mr Johnson, echoing Mr Biden, downplayed chances of securing agreement with the US before the next general election, saying: "The Americans do negotiate very hard."
Environment Secretary George Eustice told Sky News: "We still very much hope to be able to put together an agreement with the United States. We are not putting timescales on it."
"It's just not a priority for the US administration," he added.
Mr Johnson highlighted the decision to lift the ban on British beef, and Downing Street is increasingly confident that there could soon be a favourable decision lifting the export ban on lamb.
Speaking to reporters in the Oval Office before the talks, Mr Biden said: "We're going to talk a little bit about trade today and we're going to have to work that through."
He did not counter the assertion from his predecessor Barack Obama that the UK would have to join "the back of the queue" in seeking a trade deal after Brexit.
It's really clear from both sides that there is no rapid path to a trade deal - the opportunity that used to be lauded by Brexiteers and by President Trump.
Mr Johnson hinted at that realism in his curtain-raiser conversations on his way over here.
And the president pretty much confirmed that in the meeting in the Oval Office.
The UK seems no longer to want to believe, or pretend, that doing business in a major deal is top of their list.
Instead, while the government is still officially pursuing a stand-alone deal with the US there's a twin track with a more incremental approach - there have already been changes to whisky tariffs and British beef. But No 10 is now hopeful that the Americans are seriously considering changing tack on British lamb.
Read more from Laura here.
A source familiar with the government's thinking told the BBC the UK could negotiate entry into an existing trade arrangement between the US, Canada and Mexico - the USMCA - set up after former US President Donald Trump tore up its predecessor, NAFTA.
"There are a variety of different ways to do this," the source said. "The question is whether the US administration is ready. The ball is in the US's court. It takes two to tango."
Elsewhere, Downing Street said Mr Johnson and Mr Biden agreed all diplomatic and humanitarian methods must be used to stop conditions getting worse in Afghanistan.
The leaders said any international recognition of the Taliban must be contingent on the group respecting human rights.
This followed a request by the Taliban to address world leaders at the United Nations summit in New York this week.
Brexit gave the UK the freedom to strike its own trade deals - and accounting for £1 in every £6 of British trade, a pact with the US was the ultimate prize.
But Whitehall officials have for months been scrabbling for an alternative after the Biden administration indicated it was in no hurry to resume talks.
Joining the USMCA arrangement already agreed by the US, Canada and Mexico could give the UK deeper benefits on some goods and digital trade with North American economies.
But it has limited coverage of the UK's biggest strength when it comes to selling to America, namely services. Economists say the overall gains from joining USMCA may be very limited, perhaps less than 0.1% of GDP
America's price of admission may include a hurdle already encountered: standards surrounding food and agricultural goods. For President Biden is explicit that his priority is US workers, not least its farmers.
He is also clear that domestic issues take precedence. Even if the UK does want to sign up to USMCA, it may still be at the back of a queue - simply to get its application considered.
Before the meeting, Mr Biden also issued a fresh warning to the UK that peace in Northern Ireland must not be jeopardised as a result of complications caused by Brexit.
He made it clear he had concerns about the Irish border, amid continuing issues with Northern Ireland Protocol - the arrangement which helps prevent checks along the border between Northern Ireland and the Republic of Ireland.
The pair also discussed the new UK, US and Australia security pact in the Asia-Pacific region, with No 10 describing it as an example of "shared values and approach to the world".
The meeting, taking place on the sidelines of the UN summit, involved the traditional exchange of gifts.
Mr Biden gave the prime minister a framed photo of their first meeting in Cornwall at the G7 summit in June, and a White House-branded watch.
Mr Johnson presented the president with a signed copy of a book written by British astronaut Tim Peake, with an inscription expressing hopes that it "provides a reminder of what we're fighting to save as our countries tackle climate change together".
The prime minister's gift comes weeks ahead of the COP26 summit in Glasgow, which is seen as a crucial moment to bring climate change under control.
Earlier, Mr Biden announced the US would double its climate finance pledge and increase funding for developing countries to $11.4bn (£8.3bn) by 2024.
Mr Johnson said the US had "stepped up to the plate" with what he called a "massive contribution" towards the $100bn (£73bn) goal for countries to raise.
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