The deaths occurred on Sunday in the city of Gainesville in north-central Florida, 386km northwest of Stuart, which lies on the state's hard-hit Atlantic coast, rescue personnel said on Monday.

A man died at midday when he lost control of his car and hit a tree, and later a woman was killed when an oak tree fell on her mobile home, Captain Beth Hardee of Alachua County Fire and Rescue said.

Gainesville was still under driving rain and high gusting winds early on Monday, some 22 hours after the storm first hit the area, she said.

"I've lived in Florida all my life and I've never experienced a storm like this," she said.

Power company workers were struggling to restore electricity to over two million people - some radio stations put the figure as high as four million.

The remnants of the eye of Frances have moved off Florida's west coast, but "it's trying to reform. It could build up strength again" over the warm waters of the Gulf of Mexico, she said.

Two people died in the Bahamas when Hurricane Frances battered the Atlantic island chain for more than 30 hours on Thursday and Friday.