The FBI says a man suspected of fatally shooting a police officer and wounding another while fleeing the scene of a bank robbery in Mississippi has died in Arizona after being shot by police during another robbery.

"An individual who robbed a bank yesterday morning in Phoenix, Arizona, and who later was shot and killed in an exchange of gunfire with a Phoenix Police Detective, has been identified as being the same individual responsible for the attempted bank robbery in Atlanta, the robbery of the BancorpSouth in Tupelo, the shooting of Officer Joseph Maher, and the murder of Officer Gale Stauffer,” the statement said.

An earlier FBI statement said a man described as being 5-feet, 9-inches tall with a light complexion and wearing a mask entered a bank in Phoenix on Saturday, filled a bag with cash from the bank's vault, and fled the scene. The suspect then encountered the police detective who shot and killed him outside the bank.

MyFoxPhoenix.com reported that the robbery took place at a Compass Bank and was reported by a witness across the street, who saw the suspect enter wearing a white mask. MyFoxPhoenix.com also reported that the suspect was shot after he fired at the responding officers.

The suspect in the two previous bank robberies was described as being between 5-feet, 8-inches tall and 6 feet tall with a slender build. The FBI released a wanted poster Friday showing the suspect wearing a facemask, a patterned jacket, khaki pants, and tennis shoes.

The FBI said Sunday that the identification of the man killed in the Phoenix robbery was “made based upon similarities” between the robberies, “including the clothing worn by the bank robber, statements uttered by the bank robber during the robberies, and the robber's overall modus operandi, supported by other evidence and information collected during the course of this investigation.”

“Additionally, cell phone records, obtained via court order, indicated that this individual's phone was in Atlanta, Tupelo, and Phoenix when the bank robberies were committed,” the statement added.

Surveillance photos from the attempted bank robbery in Atlanta showed a man wearing a black-and-white patterned jacket tried to rob a Bank of America branch on Piedmont Road around 9:30 a.m. Monday. He was wearing a black ski mask and black gloves and carrying a handgun.

After failing to get any money from a teller, the man demanded and received an undisclosed amount of money from someone who was using an ATM in the bank's lobby. The man was seen leaving in a light gray car with no license plate, possibly a Chrysler 200.

Later that day, the suspect stole an undisclosed amount of money from the BancorpSouth in Tupelo, Miss., before fleeing in a grey sedan, according to Daniel McMullen, special agent in charge of the FBI's office in Jackson, Miss.

Officers Gale Stauffer and Joseph Maher were responding to a bank alarm and a report that the suspect had fled in a white SUV when they spotted such a vehicle stalled in traffic, McMullen said. The officers were confronting the SUV's driver when the suspect exited the gray sedan, which was stopped behind the SUV, and ambushed the officers, according to McMullen.

Stauffer died and was buried Friday after a funeral attended by as many as 1,000 people. Dozens of uniformed officers from Mississippi, Alabama, Tennessee and elsewhere attended the service.

Stauffer's wife, Beth, said her family was grateful for investigators' work and for the support they've received.

"We can truly begin the healing process, and that could not have happened without the hard work of so very many," she told reporters Sunday. "Gale would be so proud."

Stauffer's family said the strength of the community is helping them get through this rough time.

"Everybody has been so wonderful to us through this week. And, the overwhelming love and support that this community has given us has helped us make it through," his mother, Debbie Brangenberg, told WTVA-TV in Tupelo.

Tupelo police Chief Bart Aguirre told the Northeast Mississippi Daily Journal that Maher's condition has improved and he was able to walk some with assistance Friday. Maher moved out of the intensive care unit at North Mississippi Medical Center and into a private room.

The FBI had offered a reward of up to $100,000 for information leading to the identification and arrest of the man responsible for the shooting.

The Associated Press contributed to this report.