A 10-year-old girl is fighting for her life after a man whose daughter was hit with a snowball returned and sprayed bullets into a group of children.

Joseph Best, 32, was arrested in Philadelphia and remanded on charges including attempted murder.

Ebony Smith, who police say was not involved in the snowball fight, is said to be in a critical condition with a head wound.

Best's daughter was hit with a snowball as she and her friends walked past a group of girls having a "friendly snowball fight", said Captain Charles Bloom of Philadelphia police.

A scuffle then broke out among the dozen or so girls, aged from 10 to 15. The groups soon parted ways, but Best returned with an older daughter and another brawl erupted, this time between adult relatives of both groups.

Police broke up that fight, but said Best came back again hours later, leaned out the passenger side of a moving car and fired at least five shots into the group of children still playing on the street. Authorities are trying to determine who was driving.

Police said the girl who was shot had been inside a house during the scuffles.

"This little girl had nothing to do with anything. She wasn't involved in the fight," Capt Bloom said. "He just seemed to be randomly shooting into the crowd."