US President Donald Trump says is surprised Democratic presidential candidate Joe Biden chose Senator Kamala Harris as his running mate because she had been disrespectful to the former vice-president during the primary debates.

Ms Harris, 55, made history by becoming the first black woman and first Asian-American on a major party presidential ticket.

Mr Trump said Ms Harris had been “very, very nasty” to Mr Biden during the primaries.

Mr Trump also tweeted a campaign ad calling Ms Harris a “phoney” noting she had criticised Mr Biden for supporting “racist policies” when they ran against each other for the Democratic presidential nomination.

Tweet from @realDonaldTrump

“One of the reasons that it surprised me, she was probably nastier than even Pocahontas to Joe Biden,” he said on Tuesday (local time).

“She was very disrespectful to Joe Biden, and it’s hard to pick somebody that’s that disrespectful.”

But Mr Trump insisted he had hoped Mr Biden would pick Ms Harris.

“She was my No.1 pick,” Mr Trump said.

Mr Trump assailed Ms Harris for her questioning of Brett Kavanaugh over sexual misconduct allegations during his Senate confirmation hearings to join the Supreme Court.

“I thought she was the meanest, the most horrible, the most disrespectful of anybody in the US Senate,” Mr Trump said.

Vice-President Mike Pence has echoed Mr Trump’s sentiment.

“Joe Biden and the Democratic party have been overtaken by the radical left,” Mr Pence said at a Trump campaign event in Arizona on Tuesday.

“Given their promises of higher taxes, open borders, socialised medicine and abortion on demand, it’s no surprise that he chose Senator Harris.”

But high-profile people on the Democrat side of politics were much more supportive of Mr Biden’s choice.

“Joe Biden nailed this decision” former president Barack Obama said of former vice-president’s selection.

“By choosing Senator Kamala Harris as America’s next vice-president, he’s underscored his own judgment and character.”

Mr Obama called Ms Harris an “ideal partner to help him tackle the very real challenges America faces right now and in the years ahead”.

Climate activist Al Gore also said the choice of Ms Harris was a “victory for those who care about combating the climate crisis”.

Mr Gore said in a tweet that Ms Harris “has made climate and environmental justice a top priority” in her political career, and he said she would be a “strong advocate in the White House”.

Mr Gore is a former vice-president and 2000 Democratic presidential nominee who was a Tennessee senator alongside Mr Biden.

Georgia voting rights advocate Stacey Abrams congratulated Ms Harris after the announcement.

Ms Abrams tweeted that she spoke at length with Mr Biden at the weekend and again on Tuesday.

House Majority Whip Jim Clyburn said Mr Biden’s selection would energise voters ahead of the general election fight against Mr Trump.

“This is everything that we need to get people to turn out the vote,” Mr Clyburn told MSNBC Tuesday.

Known as an aggressive campaigner, Ms Harris has won statewide elections three times in California.

She built her early career as district attorney of San Francisco and was elected as the state’s attorney general.

The US President’s criticism comes as it emerged he donated twice to Ms Harris when she was a candidate for attorney general of California.

State records indicate he contributed a total of $US6000 to her campaign committee in 2011 and 2013 combined.

-with agencies