By Joseph Ax

(Reuters) - The U.S. Coast Guard on Saturday said it had suspended its search for a family whose sailboat disappeared off the Florida coast six days ago.

The Coast Guard also confirmed that two bodies recovered on Wednesday and Thursday belonged to Ace Kimberly, 45, and his 17-year-old daughter, Rebecca. Kimberly's two sons, aged 13 and 15, remain missing.

Calling it a "very difficult decision," Captain Gregory Case said he had informed friends and relatives of the Kimberly family that the Coast Guard would cease search operations.

The family was last seen on Sunday when they set sail for Fort Myers from Sarasota, Florida, in a 29-foot (9-meter) sailboat.

The vessel encountered 6-foot (1.8 m) seas on Sunday during a storm near Englewood, about 30 miles (48 km) south of Sarasota, according to authorities.

The state's Fish and Wildlife Conservation Commission will take possession of the evidence gathered by searchers, including a number of personal effects from the boat, in an effort to determine what happened.

"There may be some questions that we will never have the answers to," said Major Roger Young of the commission. "But the point of the investigation is to try to get to the bottom of what happened."

The Coast Guard has said the family had lived on the vessel for about a year. They were traveling to Fort Myers for repairs to the boat, which was in poor condition.

In addition to the Coast Guard, the search involved several other federal, state and local emergency responders. The effort covered more than 34,000 square nautical miles, Case said.

(Editing by Frank McGurty and David Gregorio)