Montenegrin police chief Zoran Brdjanin said in a video statement shared with media that the attacker was a 34-year-old man he identified only by the initials VB.

Brdjanin said the man used a hunting rifle to first shoot to death two children - aged eight and 11 - and their mother, who lived as tenants in the attacker's house in the city of Cetinje in the southeastern European nation.

The shooter then walked into the street and randomly shot 13 more people, seven of them fatally, the chief said.

"At the moment, it is unclear what provoked VB to commit this atrocious act," Brdjanin said.

Andrijana Nastic, the prosecutor co-ordinating the crime scene investigation, told journalists the gunman was subsequently killed by a passerby, and that a police officer was among the wounded.

She said nine of those killed died at the scene, with two others pronounced dead after being rushed to hospital.

Cetinje, the seat of Montenegro's former royal government, is 36 kilometres west of Podogrica, the capital of the small Balkan nation that borders Serbia, Bosnia & Herzegovina, Kosovo and Albania.

Prime Minister Dritan Abazovic wrote on his Telegram channel that the incident was "an unprecedented tragedy" and urged the nation "to be, in their thoughts, with the families of the innocent victims, their relatives, friends and all the people of Cetinje".

President Milo Djukanovic said on Twitter he was "deeply moved by the news of the terrible tragedy" in Cetinje, calling for "solidarity" with the families who lost loved-ones in the incident.

Australian Associated Press