"Our priority today is search and rescue," state Governor Charlie Crist said, after declaring a state of emergency in four affected counties.
There are fears that the death toll will rise further.
The storms hit before dawn on Friday, damaging hundreds of houses and leaving more than 10,000 people without power.
All the deaths occurred in the central Lake County, where some of the worst of the damage was reported.
House-to-house search
Rescue teams with dogs are continuing to comb through piles of debris in the most affected areas.
In pictures: Florida tornadoes
Officials say the priority is finding survivors who may be trapped, but also to recover bodies.
"We are doing house-to-house searches at this time," Lake County's emergency services' chief Jerry Smith said.
Officials say it could take several days to determine the exact number of dead.
Shelters have been opened to house the affected residents.
'Like a train'
The storms hit during the night, at about 0315 (0815 GMT), when most residents were sleeping.
"We have complete devastation of homes, of businesses, religious institutions"
Residents spoke of "almost continuous lightning", likening the storm to a freight train that hit their homes.
"It woke me out of a dead sleep," David Wholly told the Orlando Sentinel newspaper.
"I heard the noise, and it sounded like a train coming and I ran to the bathroom. The tree went right through the bedroom window where my head was."
Officials later confirmed that 13 people were killed in the Paisley and six in the Lady Lake areas of Lake County. Among the dead were several children.
Dozens of mobile homes and church in Lady Lake were demolished.
'Shocked but grateful'
Hilary Hague, who lives in The Villages retirement complex near Lady Lake, told BBC News that the storms had started with severe lightning, followed by heavy rain.
She said it got worse later " when there was almost continuous lightning".
"We went outside to check, and heard a huge whooshing sound so went back inside. We thought nothing more about it until we saw the damage this morning," she said.
While she and her husband had escaped relatively lightly, "houses nearby lost all their windows and roofs, and there were cars turned up onto their roofs".
She said local residents were "quite shocked - this is not a usual occurrence in this area - but also grateful" that they had apparently escaped the deaths and injuries suffered elsewhere.
In 1998, tornadoes killed 42 people in Florida in what was the state's worst storm on record.
You can send your pictures and moving footage to yourpics@bbc.co.uk or text them to 07725 100 100
When taking photos or filming please do not endanger yourself or others, take unnecessary risks or infringe any laws.
The BBC may edit your comments and cannot guarantee that all emails will be published.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~50~RS~)