Donald Trump told Theresa May she should sue the EU rather than negotiate over Brexit, she has told the BBC.
The US president said on Friday at a joint press conference he had given her a suggestion - but she had found it too "brutal".
Asked by the BBC's Andrew Marr what it was he had said, she replied: "He told me I should sue the EU - not go into negotiations."
She defended her blueprint for Brexit and urged her critics to back it.
She said it would allow the UK to strike trade deals with other nations, end free movement of people, and end the jurisdiction of the European Court of Justice.
A White Paper published on Thursday fleshed out details of her plan, which advocates close links with the EU on trade in goods, but not services.
Before the paper was published, Brexit Secretary David Davis and Foreign Secretary Boris Johnson resigned, saying it would not deliver the Brexit people voted for in the 2016 referendum.
Mrs May laughed off the president's legal action suggestion, saying she would carry on with negotiations, but added: "Interestingly, what the president also said at that press conference was 'don't walk away'.
"Don't walk away from those negotiations because then you'll be stuck. So I want us to be able to sit down to negotiate the best deal for Britain."
Donald Trump told the Sun newspaper Mrs May's proposals would "probably kill" a trade deal with his country.
But hours later he said a US-UK trade deal would "absolutely be possible".
Leading Tory Brexiteer Jacob Rees-Mogg has called the White Paper a "bad deal for Britain". He says it would lead to the UK having to follow EU rules with no say in how they are made.
He told the BBC's Sunday Politics: "The government unfortunately believes that Brexit is not a good thing in itself, it seems to think it has to be tempered by non-Brexit."
He said Mrs May, who campaigned to keep Britain in the EU in the 2016 referendum, had failed to grasp the "enormously positive" opportunities offered.
He described her as a "Remainer who has remained a Remainer".
He also said she would have to change her policy in order to get it through Parliament, without having to rely on Labour votes.
Mrs May urged Brexiteers in her own party to "keep their eye on the prize" of Brexit - and said her plan was the only workable way to deliver it.
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