Police couldn't say whether the shootings at a cultural center Saturday afternoon and in front of the synagogue early Sunday were connected, but didn't rule it out.
In both shootings, the gunman got away, AP reported.
"We are looking for two perpetrators," police spokesman Allan Wadsworth-Hansen told reporters.
The first shooting happened shortly before 4 p.m. Saturday. Danish police said the gunman used an automatic weapon to shoot through the windows of the Krudttoenden cultural center.
A 55-year-old man attending the event was killed, while three police officers were wounded. Two belonged to the Danish security service PET, which said the circumstances surrounding the shooting "indicate that we are talking about a terror attack."