(Reuters) - A Florida man shot and killed his 1-year-old daughter and critically wounded his 7-year-old son before fatally shooting himself on Wednesday after an argument with the children's mother, law enforcement officials said.

Timothy Hollis, 32, is accused of shooting his two children at about 1:30 a.m. EDT in the city of Dania Beach, just outside Fort Lauderdale, the Broward County Sheriff's Office said in a statement.

Hollis and the 34-year-old mother of his children had been arguing earlier in the night, the statement said. They drove to the home of family members in Dania Beach, where the mother got out of the vehicle to get help from relatives.

"Hollis remained in the car with the two kids," the statement said. "Shots were fired."

The children's mother and family members ran to the car to find the boy lying "on the street with serious life-threatening injuries" it said.

The bodies of Hollis and the 1-year-old daughter were on a nearby sidewalk.

The boy was taken to a local children's hospital.

It was not immediately clear what had caused the argument between the parents.

The deaths came the same week an Arizona woman was found dead inside her Phoenix-area home with the bodies of her 17-year-old son and 12-year-old daughter. The mother is believed to have shot her two children before turning the gun on herself.

(Reporting by Laila Kearney; Editing by Alan Crosby)