MIAMI -- The man who police said attacked and tried to rape a woman at International Mall last week is under arrest.

The attack allegedly happened in the parking lot of Macy's at the mall. Police said the 30-year-old woman was putting her shopping bags into her car when a man, whom they believe to be 28-year-old Steve Rodriguez, tried to sexually assault her. The man had his pants down to his knees, police said.

"This sick individual had his pants down and was fully exposed, ready to rape the victim as soon as he could, not caring about his surroundings, that this was a mall full of shoppers and in broad daylight," said Sgt. Ralph Gracia of the Doral Police Department.

Police said the 6-foot-3-inch tall, 200-pound attacker got more than he bargained for. The victim, who is described as petite, put up a fight.

"Unfortunately, he fell into the hands of a tornado, and she went after him. She fought and fought, and he finally realized, 'She is too much for me,'" Gracia said.

Once the woman fought him off, the attacker got into his car and tried to drive away. The woman got into her car, and surveillance video shows her chasing the attacker, but he escaped.

Police tracked down the suspect by a license tag number the victim gave them. Investigators said the tag number matched Rodriguez's car, and he resembles a suspect sketch officials had released.

According to police, Rodriguez said he was in the vicinity and was driving his car around the time the attack happened, but he said he has never met the victim.

The victim identified Rodriguez as her attacker.

Rodriguez faces three charges, including kidnapping, attempted sexual battery and false imprisonment. He is being held without bond.

Police said that Rodriguez does not have a criminal record, but that that does not mean he has not committed other crimes.

"We are also asking the public that if anyone recognizes this man, this individual, and they were a victim but were just afraid to come forward, to please contact the city of Doral Police Department," Gracia said.