Senior Republicans in the US have distanced themselves from Donald Trump after he said Democratic rival Kamala Harris was “mentally impaired” while also saying she should be “impeached and prosecuted” in an ugly escalation of his personal attacks.

Trump’s rally in Erie, Pennsylvania on Sunday (local time) took on similar themes at an event a day earlier, which he described as a “dark speech”.

The Republican presidential nominee told a cheering crowd that Harris was responsible for an “invasion” at the US-Mexico border and “she should be impeached and prosecuted for her actions”.

“Crooked Joe Biden became mentally impaired,” he said.

“Sad. But lying Kamala Harris, honestly, I believe she was born that way. There’s something wrong with Kamala. And I just don’t know what it is, but there is definitely something missing. And you know what, everybody knows it.”

With just over a month until the election, Trump is intensifying his use of personal and offensive attacks, even as some Republicans say he would be better off sticking to the issues.

Former Maryland governor Larry Hogan, who is running as a Senate Republican candidate, said the comments were “outrageous and unacceptable”.

“I’ve already called him out, when he had the one interview where he was questioning her racial identity, and now he’s questioning her mental competence,” he said.

Hogan, considered a moderate Republican, said Trump’s remarks were “insulting not only to the Vice President, but to people that actually do have mental disabilities”.

“I’ve said for years that Trump’s divisive rhetoric is something that we could do without. I think he’s his own worst enemy,” Hogan said.

South Carolina Republican senator Lindsey Graham also pushed back on the remarks.

“I just think the better course to take is to prosecute the case that her policies are destroying the country,” he told CNN.

“I’m not saying she’s crazy, her policies are crazy.”

Trump’s suggestions that political enemies be prosecuted are particularly notable for their departure from norms in the US, where the justice system is supposed to be protected from political influence.

In recent weeks, he has threatened prosecutions of Google for allegedly giving priority to “good stories” about Harris and Meta CEO Mark Zuckerberg.

He has also long threatened legal action against his rivals, including President Joe Biden and his 2016 rival Hillary Clinton.

This month he vowed to jail those “involved in unscrupulous behaviour” this election, including election workers, lawyers, political operatives, donors and voters, yet again attempting to sow doubt about the integrity of the election.

On Sunday, Trump acknowledged he might lose the November 5 presidential election.

“If she (Harris) wins, it’s not going to be so pleasant for me, but I don’t care,” he said.

Trump has derided Harris, the first black woman and person of South Asian descent to lead a major party ticket, as “stupid,” “weak,” “dumb as a rock” and “lazy”.

His allies have pushed him publicly and privately to talk instead about the economy, immigration and other issues.

Harris has not commented on Trump’s recent attacks but has said when asked about other comments that it was the “same old show”.

“The same tired playbook we’ve heard for years with no plan on how he would address the needs of the American people,” she said.

At the rally in Erie, Trump said the “invasion” would end and deportations would begin if he took office.

“Thousands of migrants from the most dangerous countries are destroying the character of small towns and leaving local communities in anguish and in despair,” he said, talking about communities in the battleground states of Wisconsin, Michigan and Pennsylvania.

In August, the GOP leader said he was “entitled” to personal attacks against Harris.

“As far as the personal attacks, I’m very angry at her because of what she’s done to the country,” he said.

“I’m very angry at her that she would weaponise the justice system against me and other people, very angry at her. I think I’m entitled to personal attacks.”

-with AAP