A police officer and a courthouse staff member both died in the attack, while others have been injured, CNN reported.
Police have killed two assailants and are hunting a third, according to the news agency.
Read alsoTurkey extends state of emergencyTurkey is still reeling from the New Year's attack on an Istanbul nightclub which left 39 people dead.
According to Anadolu, at least 69 others were hurt while the gunman remains at large.
Police have detained 34 suspects, excluding those picked up in raids Thursday, the news agency reports.
Read alsoManhunt for Istanbul gunman intensifiesISIS claimed responsibility for the attack in a statement posted to Twitter, but CNN cannot independently verify it. The terror group boasted of carrying out the first major terrorist attack of 2017.
Izmir, a busy port on the Aegean Sea, is Turkey's third-largest city, home to more than two million people.
