NAPLES, Fla. -- Three men reportedly overheard talking about a terrorist plot were pulled over and detained for 17 hours Friday before authorities said the men were apparently kidding around and released them.

"If this was a hoax, they will be charged," Collier County Sheriff Don Hunter said angrily after an all-day search of the men's two cars turned up no sign of explosives.

It was unclear what charges, if any, the men might face in Florida or Georgia, where a woman told authorities she heard them plotting at a restaurant Thursday morning. After their release, the three drove to a rest stop, where they told reporters they were medical students heading to Miami for training and denied making any comments or jokes about terrorism.

One man, who has a long beard and wore a skull cap, said the woman who reported them to police may have been influenced by his appearance. They declined to give their names.

The cars were stopped after the Georgia woman reported overhearing three men who appeared to be of Middle Eastern descent making "alarming" comments during breakfast at a restaurant in Calhoun, Ga., said Mickey Lloyd of the Georgia Department of Public Safety.

According to authorities, one of the men said Americans "mourned on 9-11 and they are going to mourn again on 9-13." They also said the target of "possible terrorist activities" was in the Miami area.

Georgia officials issued an alert based on the woman's report and the cars were stopped at 1 a.m. after one went through the Interstate 75 toll booth east of Naples, authorities said.

The men were detained in a van while authorities used dogs and a robot to go through the cars.

A federal law enforcement official in Washington, who spoke on condition of anonymity, said the men are of Jordanian, Iranian and Pakistani descent. Authorities said one is a U.S. native, another a naturalized citizen and the third has a valid visa.

Relatives of the men criticized the investigation, suggesting they had been singled out because of their heritage. One was identified by his father as Omar Chaudhary, 23, who was born in Detroit to Pakistani immigrants.

"I don't know what the lady in the restaurant heard or assumed. She must have had some kind of prejudice," Javed Chaudhary said from his home in Kansas City, Mo. "My son was born and raised here. I feel like we don't have freedom here anymore. Anybody can call anybody to make any kind of accusation. And the authorities treat you like you are a criminal."

Hana Gheith of suburban Chicago also said she didn't believe the report about her brother, 27-year-old Ayman Gheith. She said he was driving to Miami with friends to find an apartment before starting a training program at a hospital.

The woman who reported the comments is Eunice Stone of Cartersville, Ga., a 44-year-old nurse who told Fox News Network that she was eating at a Shoney's restaurant in Calhoun when she heard the men talking.