President Trump doubled down on his criticisms of London Mayor Sadiq Khan during a press conference alongside outgoing British Prime Minister Theresa May, a jab that Karl Rove said he was better off avoiding.

Trump and May briefly answered questions from reporters following a joint news conference on Tuesday, where the president was asked about his controversial tweets directed towards Khan on Monday.

"He's done a poor job, crime is up, a lot of problems," Trump reasserted on Tuesday.

During an appearance on "America's Newsroom" following the news conference, Rove said Trump should have ignored Khan's criticism.

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"This is the one thing I think the president will be better off not punching down," said Rove, a Fox News contributor and former White House deputy chief of staff under George W. Bush.

"I think it would have been better to have left it in the hands of the British prime minister who answered by basically ignoring the mayor which is how he deserves to be treated."

Rove added that President Trump tends to take things personally, which can be an "advantage or a disadvantage."

Trump went on to say that Khan should not have spoken out against a leader for the United States - a country that "can do so much good for the United Kingdom" - before saying the first Muslim mayor of London is a "negative force."

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The two politicians have traded jabs over Twitter throughout the duration of President Trump's U.K. visit, with Trump labeling the mayor as a "stone cold loser" as he arrived in London. Khan responded by telling BBC that the president's insults reminded him of "the sort of thing an 11-year-old would do."