Chief negotiators Michel Barnier and the UK's David Frost met last week.
Trump, a fervent supporter of Brexit and Johnson and a frequent critic of the EU, has said that he wants to get a US-UK trade deal done quickly.
The proposed law, which overrides parts of the Brexit treaty relating to trade in Northern Ireland, could torpedo already fraught trade talks with the EU.
House of Commons MPs gave their initial approval to the UK Internal Market Bill by 340 votes to 263, clearing the way for four days of detailed scrutiny.
The House of Commons will hold its first debate over a bombshell new bill introduced by Johnson's Conservative government.
Brexit tensions and uncertainty over the US presidential election are keeping gains in check.
The EU is worried that post-Brexit Britain could undercut its own food standards, as well as rules on state aid for companies.
The pound was struggling to fight its way out of a trough as sparring between Britain and the EU raised the prospect they will not reach a trade agreement.
The UK bill has further complicated the already messy Brexit process, as Britain unpicks nearly 50 years of European integration.
Britain is racing to agree a trade deal with Brussels as the clock ticks down to a crunch EU summit in mid-October.
US traders returned from a long weekend to resume the selling that sent shudders through markets last week as they fretted over lofty valuations of equities.
Talks have been deadlocked for months over issues such as the extent of EU access to UK fishing waters, state aid and fair competition rules.
Britain remains bound by EU rules while it tries to thrash out new terms of its relationship.
Britain followed through on the results of a deeply divisive 2016 referendum and left the EU after almost half a century of integration on January 31.
The chief Brexit negotiators of UK and EU ruled out a deal framework by the end of July because of fundamental gaps in major areas.
The accusations came even before the publication of a long-awaited British parliamentary report into alleged Russian interference in the 2016 Brexit vote.
British and EU negotiators are making slow progress in working towards an agreement on future relations.
London will host EU negotiator Michel Barnier after a round of face-to-face talks ended a day early last week in Brussels.
Merkel's last major role on the international stage comes as the 27-member club faces its deepest recession since World War II.
The new round of talks in Brussels will be the first to be held face-to-face since the coronavirus shutdown.
It was Johnson's first personal involvement in the talks, which began just weeks after Britain left the EU on January 31 after 47 years.
Monday's video conference with European Commission president Ursula von der Leyen and European Council chief Charles Michel will review progress in the talks.