McMullen also said there were "numerous similarities" between the three bank robberies, including the clothing worn by the suspect, statements he made during the incidents and his "overall modus operandi."
"This investigation is not over," McMullen said at a news conference in Tupelo. "There are numerous leads which we must continue to follow and questions which we must answer."
On Monday afternoon, the suspect stole an undisclosed amount of money from the BancorpSouth in Tupelo before fleeing in a grey sedan, according to McMullen.
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."
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 Phoenix shooting happened Saturday morning at a Compass Bank branch in the near-northwest part of the city after someone reported seeing a man run into the bank while wearing a mask.
The first officer to arrive saw the man leave the bank with a bag and a handgun.
"The officer drew his service weapon and began giving the suspect commands at which time the suspect raised his weapon and began firing at the officer," police spokesman officer James Holmes said in a statement.
A detective who had just arrived at the scene shot the suspect, who was pronounced dead after being taken to a Phoenix hospital.
Holmes said no officers or bank employees were injured. He says the two officers involved will be placed on standard administrative leave.
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.