The top two Republicans in Congress have broken their silence about Donald Trump’s dinner last week with the rightwing extremist Nick Fuentes, saying the Republican party has no place for antisemitism or white supremacy.

The Senate Republican leader, Mitch McConnell, and Kevin McCarthy, who may become House speaker in January, had not commented previously on the 22 November meeting.

Trump began his 2024 bid for the White House on 15 November and is Republican voters’ top choice, according to polling.

“There is no room in the Republican party for antisemitism or white supremacy and anyone meeting with people advocating that point of view, in my judgment, are highly unlikely to ever be elected president of the United States,” McConnell told reporters on Tuesday – without mentioning Trump by name.

Asked if he would support Trump should he become the party’s 2024 nominee, McConnell said: “That would apply to all of the leaders in the party who will be seeking offices.”

McCarthy was pressed by reporters after White House talks with Joe Biden.

“I don’t think anybody should be spending any time with Nick Fuentes,” said the House minority leader. “His views are nowhere within the Republican party or within this country itself.“

Trump has said the encounter at his Mar-a-Lago resort in Florida was inadvertent but the meeting has drawn rare criticism from Republicans, some of whom accused Trump of empowering extremism. Tuesday’s comments were the first about the meeting by McCarthy and McConnell.

Fuentes has been described as a white supremacist by the US justice department. The Anti-Defamation League said Fuentes once “jokingly denied the Holocaust and compared Jews burnt in concentration camps to cookies in an oven”.

While president, Trump was broadly criticized for not explicitly condemning white nationalists whose August 2017 rally in Charlottesville, Virginia, was seen as having provoked violence with counter-protesters, one of whom was killed.

“You also had people that were very fine people on both sides,” Trump said.

Trump’s former vice-president, Mike Pence, on Monday called for an apology for the meeting with Fuentes.

“President Trump was wrong to give a white nationalist, an antisemite and a Holocaust denier a seat at the table, and I think he should apologize,” Pence told NewsNation.

Fuentes attended the dinner with Ye, the musician formerly known as Kanye West, who has also drawn widespread criticism for antisemitic comments.