"We routinely investigate when our own bullets lead to a death," a police spokesman told news agency TT.
Lena Olsson of the Left Party told TT that police should review their weapons use and consider replacing sharp ammunition with tazer guns.
"There have been many fatal shootings lately, including of psychologically unstable people," said Olsson.
Since 1995, 18 people have died in Sweden after being shot by police, three of them this year.
The first attack in Varberg happened at around 10:00 AM on Sunday. About an hour later a woman in her mid-eighties was stabbed and died on the spot. A younger man was also wounded.
Police said they fired two warning shots when they arrived on the scene, but the attacker refused to stop. He was then shot and died later while being treated at Varberg hospital.
The two men injured in Varberg will be questioned on Monday.