By Alex Dobuzinskis

(Reuters) - A man has been arrested on suspicion of being involved in the killing of two homeless men and attacks on two other transients in San Diego this week, the mayor said in a statement.

The suspect, identified as Anthony Alexander Padgett, 36, was arrested on Thursday in the suburb of Chula Vista and booked on suspicion of two counts of murder, two counts of attempted murder and one count of arson, City News Service reported.

Police and prosecutors did not immediately return calls seeking comment.

"Thanks to the tireless work by the San Diego Police Department and incredible help from the public, we have a suspect in custody," San Diego Mayor Kevin Faulconer said on Twitter late on Thursday.

Investigators believe Padgett is the "person of interest" they initially described who was seen at a convenience store shortly before the first victim's body was found on Sunday morning, local media reported.

Police had publicly released surveillance photos and video of the person.

It was not immediately clear if the suspect had obtained an attorney and he could not be reached for comment.

After the first attack on Sunday, the body of a homeless man was discovered on fire between a highway and train tracks in the Mission Bay area of San Diego, police said. The victim has been identified as 53-year-old Angelo De Nardo and an autopsy determined he was killed before being set ablaze, City News Service said.

On Monday before dawn, a 61-year-old homeless man was discovered bleeding, with trauma to his upper body, less than 4 miles (6 km) south of the first attack, police said. He was taken to a hospital in critical condition.

Police also said that on Monday morning, another homeless man was discovered with severe wounds to his upper body and was pronounced dead at the scene near tennis courts in the Ocean Beach neighborhood. The victim has since been identified as 41-year-old Shawn Longley, according to City News Service.

Early on Wednesday, a homeless man was found critically wounded when he was set on fire outside a downtown San Diego apartment building, police said. Police had said before the arrest that all four attacks appeared to have been the work of one person.

(Reporting by Alex Dobuzinskis in Los Angeles; editing by Grant McCool)