Mr Trump said ahead of his visit that he could meet Boris Johnson, who resigned earlier this week over Mrs May's Brexit plan.
A rebellion by Eurosceptic backbenchers could wipe out Mrs May's majority when the bill returns to the House of Commons on Monday, in what would be the first significant test of strength for her Brexit critics. French Prime Minister Edouard Philippe said "the worst" scenario of Britain crashing out of the bloc without a deal was still a possibility.
"What we're doing is delivering on the vote of the British people. that's what our proposal does", May told reporters when asked about Trump's comment.
U.S. President Donald Trump, who arrived in Britain on Thursday at the start of a working visit, said before the white paper's publication he was not sure May's approach was what Britain voted for in the 2016 referendum.
Some seven weeks of talks lay head for European Union lead negotiator Michel Barnier and the British Brexit team.
The EU has "equivalence" regimes which provide limited access for some of non-EU partners to some areas of EU financial services markets.
The EU's chief negotiator, Michel Barnier, said he would analyse the paper with member states and the European Parliament and repeated the bloc's offer for an ambitious free trade agreement with "effective cooperation" on issues.
In a policy paper, the government will outline proposals to allow Britain to maintain close economic and security ties with the European Union even after it leaves the bloc in March.
Although UK officials insist that the proposal is different to other pacts between the EU and third countries, it is essentially closest to the EU-Ukraine Association Agreement.
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Looking at the reception to May's paper from the Tory leader's own party, the Guardian reported that "almost all the reaction from Conservative MPs was either sceptical, or downright hostile", noting particular "alarm" being expressed over the role that the European Court of Justice (ECJ) looks set to continue playing in Britain's affairs post-Brexit.
They will hold talks at the Prime Minister's country residence of Chequers on Friday where Russia, Brexit and the Middle East will top the agenda.
Unrest among Brexiteers over the plan means the PM may have to rely on support from outside her party to push it through parliament.
The British proposals on customs, which are complex and untested, are also likely to run into trouble in Brussels.
The amendments would also: ensure "reciprocity of customs collection" to treat Britain and the EU as equals; put into law that Britain will not be part of the EU's Value-Added Tax regime; and require that any customs union would be created by primary legislation. Britain would accept their rules and contribute to their costs, the white paper said.
While ending freedom of movement of people, Britain will try to ensure that tourists can travel freely around Europe and will try to make its immigration policy better cater for business needs.
Appearing before the Home Affairs Select Committee, Javid said: "There will be no automatic right for anyone in the European Union, or anyone else for that matter, to just make a unilateral decision that they can just hop on a plane or ferry and just come and work in the UK".
The EU maintains that existing British red lines - no jurisdiction of the European court of justice, no free movement of people - mean the only option is a free-trade agreement, similar to those Brussels negotiated with Canada or Korea - a point of conflict with the United Kingdom that is subtly restated in Barnier's tweet.