At least two people have been killed and two others injured in shootings at a kebab shop and near a synagogue in the east German city of Halle.
One person was arrested, but police believe at least one other may have fled the area in a vehicle.
At least one gunman was seen wearing a military-style outfit carrying several weapons, witnesses say.
Reports suggest there was also a shooting incident in Landsberg, some 15km (9 miles) east of Halle.
The situation remains unclear and local residents in both areas have been told to stay inside their homes.
Two injured people with gun wounds are having surgery at Halle's university hospital, a spokesman told AFP news agency.
German federal prosecutors have said they are taking over the investigation because of the "particular importance of the case".
What do we know about the attacks?
A man was killed in a Turkish kebab shop, Halle police spokesman Ralf Karlstedt said.
A second victim, who is a woman, reportedly died on a street close to a Jewish cemetery and synagogue.
It remains unclear if the two attacks were carried out by the same person.
Police say a suspect was arrested after fleeing the scene, but their identity and motive has not yet been released.
Max Privorotzki, leader of the local Jewish community, told Der Spiegel magazine that a gunman had tried to get into a Halle synagogue where between 70 and 80 people were inside.
One witness said one attacker "dressed like a policeman… fully armed" had thrown a petrol bomb or grenade over a cemetery wall.
The violence came as Jews celebrated Yom Kippur, Judaism's holiest day.
A witness at the kebab shop told German n-tv news that a gunman in camouflage had opened fire on the venue.
"The man came up to the doner shop, he threw something like a grenade, it didn't explode, and he opened fire with an assault rifle… I hid in the toilet," the witness told a TV reporter near the scene.
A video posted on social media appears to show at least one suspect, wearing a helmet, firing into the air from behind a car.
Shane Smith, a tourist from New Zealand, heard six loud shots from the flat where he was staying, he told the BBC.
He later witnessed a vehicle speeding up a local road, pursued by a police car with a damaged window.
Local police have told local residents to stay calm and be wary of false reports of further incidents.
A minute's silence was held for the victims in the European Parliament in Brussels.
"Together with you, I would like to express my sympathies to the German police forces, the German people and the German Jewish community," European Parliament President David Sassoli said, leading the tribute.