US President Donald Trump said the US and UK have the “greatest alliance the world has ever known” in a news conference with Theresa May, according to BBC.
The prime minister said they had a “great relationship” that they should “build on”.
The pair have been holding talks at No 10, with contentious issues such as business with Huawei on the agenda.
Labour leader Jeremy Corbyn urged Mr Trump to “think on about peace” as he addressed protesters in Westminster.
During a breakfast meeting at St James’s Palace earlier on Wednesday, Mr Trump said he believed there was scope for further expansion of trade between the US and the UK.
“I think we will have a very, very substantial trade deal,” he told Mrs May.
“This is something you want to do and my folks want to do,” he added. “Stick around. Let’s do this deal.”
BBC assistant political editor Norman Smith said that Mr Trump’s remark to “stick around” was meant almost as a pleasantry rather than a serious plea for Mrs May to reconsider her plan to stand down.
“It’s just trying to make this a little bit easier for her,” Mr Smith said.
He added that although Mr Trump “talks a good game” over a trade deal, the UK is likely to be in for a “slow haul”, with most deals taking around 10 years.
The meeting of five British and five American firms, senior ministers and officials was held in a bid to boost trade links.
Mrs May said there were “huge opportunities” for Britain and the US to work together in the future.
“It is a great partnership but I think a partnership we can take even further,” she told the president, adding: “Of course that is with a good bilateral trade deal.”
The US president is also set to hold talks with Conservative leadership hopeful Michael Gove, according to sources close to the environment secretary.
Mr Trump praised Mr Gove’s leadership rival Boris Johnson ahead of his visit to the UK.