Theresa May has rejected Donald Trump’s assessment of her Brexit deal, insisting the UK will be able to strike new trade agreements – including with the US – after leaving the EU.

Speaking in Wales on the first leg of a UK-wide tour to promote the deal directly to the British public, the prime minister said: “We will have the ability, outside the European Union, to make those decisions on trade policy for ourselves. It will no longer be a decision being taken by Brussels.

“As regards the United States, we’ve already been talking to them about the sort of agreement we could have with them in the future.”

Why does Donald Trump oppose Theresa May's Brexit deal? Read more

Trump’s comments on Monday that the Brexit agreement “sounds like a great deal for the EU” came as No 10 attempted to marshal support for the arrangement in the face of a chorus of condemnation at Westminster.

The US president said: “I think we have to take a look at, seriously, whether or not the UK is allowed to trade.

“Because, you know, right now, if you look at the deal, they may not be able to trade with us … I don’t think that the prime minister meant that. And hopefully she’ll be able to do something about that.”

Play Video 0:40 Trump says UK ‘may not be able to trade with US’ under May’s Brexit deal – video

May’s spokesman repeatedly insisted on Tuesday that it was clear “in black and white” in the political declaration forming part of the Brexit deal that the UK will have the power to make new trade agreements.

Asked whether the UK’s commitments not to lower environmental standards and other regulations below EU levels will hinder trade with the US, the spokesman added that parliament will have a say on future deals.

“Parliament will want to take a view in relation to all trade deals, in particular looking at the standards which the UK has in areas such as animal welfare,” he said.

The government believes MPs would be unlikely to support any deal that allowed the US to sell chlorinated chicken into the UK, for example.

Privately, senior government sources insisted they were relaxed about Trump’s intervention, which they regarded as the latest example of a tough-talking negotiating style from the man behind The Art of the Deal.

May’s spokesman said she would not hold a one-to-one meeting with Trump on the sidelines of the G20 summit in Argentina this weekend.

“It’s not something that we have requested; the PM’s diary is agreed in advance and she’s meeting with a number of world leaders,” he said. “We’ve met the president on a number of occasions in recent months.”

With a fortnight to go until May presents the Brexit agreement to the House of Commons for approval, she visited a country fair in Wales on Tuesday and will travel to Northern Ireland later in the day to meet local politicians.

While in Northern Ireland, she hopes to underline the fact that the Democratic Unionist party, MPs from which have angrily rejected the Irish backstop, do not speak for everyone in the province.

Downing Street hopes making the argument for her deal publicly could help build up backing among voters and create a supportive backdrop for the meaningful vote on 11 December.

But with more than 90 Conservative MPs expected to vote against the deal, it looks highly likely the government will lose.

Trump had previously raised doubts about May’s negotiating prowess when he came to the UK on a working visit in July. The prime minister later revealed he had suggested she “sue” the EU.