Jeremy Corbyn has criticised the US president over his endorsement of Boris Johnson as a future prime minister.
Donald Trump was alongside Theresa May when he said Mr Johnson, who quit her cabinet this week, would make a "great prime minister".
Labour leader Mr Corbyn said: "With the greatest respect, it's not his business who the British prime minister is."
He also criticised the US president's attacks on London's mayor Sadiq Khan as "completely unacceptable".
Mr Corbyn went on to address crowds of protesters in Trafalgar Square, telling them: "We are asserting our right to demonstrate, our right to free speech."
He added that the demonstration's message was "one of solidarity": "When we unite together with common objectives, we can all win."
Earlier on Friday Mr Trump insisted he had not criticised the prime minister in an interview with The Sun newspaper, at joint press conference with her at Chequers.
After a difficult week for Mrs May, whose proposals for trade with the EU after Brexit sparked two cabinet resignations - including Mr Johnson's - Mr Trump also told the newspaper the former foreign secretary has "got what it takes" to lead the UK.
Asked about the remarks, the president said: "He's been very nice to me. He's been saying very good things about me as president.
"I think he thinks I'm doing a great job. I am doing a great job, I can tell you, just in case you haven't noticed.
"Boris Johnson, I think, would be a great prime minister."
But Mr Corbyn said the president had exhibited "very strange behaviour" by rowing back on comments he had made to the Sun about the prospects of a future UK-US trade deal, having initially said the prime minister's Brexit plan would "probably kill" a future trade deal with the US.
The Labour leader went on: "It's a very strange thing to do, to come on a visit to another country, to meet that country's prime minister and then announce you would like to see as her successor, a person who has just resigned from her government.
"Johnson resigned for the reasons he gave, that is Johnson's business, that is Theresa May's business to respond to. It really isn't anything to do with Donald Trump."
He also criticised Mr Trump's verbal attacks on Sadiq Khan, who the president said had been doing a "terrible job" following terrorist attacks in London. Mr Khan has said he will not rise to the "beastly" accusation.
Mr Corbyn said: "It is quite without precedent and quite unreasonable the way Trump treats London and treats Sadiq Khan."
He went on: "When a terrible incident happened ... then surely you should recognise that the police and community have a job to do, and what Sadiq has sought to do is bring people together in unity to keep London together, just as happened after 7/7 all those years ago."
He added: "Personally I don't think we should have been rolling out the red carpet for Donald Trump."