Former New York City mayor Rudy Giuliani stepped up his criticism of Black Lives Matter on Monday, saying he saved "a lot more black lives" during his time in office than the movement.

The Republican made the comments during a morning appearance on Fox and Friends, where he alluded to his tough-on-crime policies while leading New York and a significant drop in the murder rate during his tenure as mayor.

"I believe I saved a lot more black lives than Black Lives Matter. I don't see what Black Lives Matter is doing for blacks other than isolating them," he said. "All it cares about is the police shooting of blacks. It doesn't care about the 90 per cent of blacks that are killed by other blacks."

Giuliani also repeated to Fox an assertion that he first made Sunday on CBS' Face the Nation, where he stressed that black children face a greater threat from other black children than from police.

He said even the term "black lives matter" is racist.

"It's inherently racist because, number 1, it divides us. All lives matter," he said Monday.

Giuliani said he understands that police officers can act improperly and the reasons why the black community may distrust police, but added that he believes the American people are getting the "wrong impression" on the issue because of a continued focus on the Black Lives Matter movement.

Alicia Garza, a co-founder of the official Black Lives Matter group, responded to Giuliani's remarks Monday during an appearance on MSNBC.

"To be honest, he shows a real lack of understanding about what racism actually is," she said. "And then to chastise black people to solve a problem in our communities that is actually rather prevalent in every community, is increasingly and incredibly short-sighted."

Black Lives Matter is focused on "ending violence in our communities," she said.