The governor of Florida, Rick Scott, has said pregnant women are to be warned not to travel to a Zika-affected part of Miami.
He called for an emergency response team to be set up, to investigate and combat the virus's spread.
Another 10 cases probably contracted locally have been identified.
The illness, which is most commonly transmitted by mosquitoes, is linked to defects including small-head syndrome, or microcephaly, in newborns.
On Saturday, England's public health agency advised mums-to-be to postpone non-essential travel to Florida.
At that point, only four cases of Zika that were believed to have been contracted from mosquitoes within Florida had been confirmed there. They were thought to be the first of their kind in the US.
Other Zika cases were among people returning from infected areas overseas.
The 14 latest Florida cases may have come about because the victims were bitten by mosquitoes that had themselves became infected by biting people who had brought the virus back from their travels to the Caribbean and South America.
Mr Scott said the new warning would advise women who were pregnant or trying to get pregnant to avoid a square mile area just north of central Miami.
The Centers for Disease Control and Prevention would issue the travel notice, he said.
The area runs between NW 5th Avenue to the west and US 1 to the east, and NW/NE 38th Street to the north and NW/NE 20th Street to the south.
Mr Scott said: "Florida has a proven track record of success when it comes to managing similar mosquito-borne viruses.
"While I encourage all residents and visitors to continue to use precaution by draining standing water and wearing bug spray, Florida remains safe and open for business."
Of the 14 individuals identified, two are women and 12 are men.
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