"Gunmen have killed a father and his five sons from Tikrit. They were shot in the head," an interior ministry source said.
A police colonel said the victims' family had been displaced by violence in Tikrit's Salaheddin province, parts of which are controlled by the Islamic State jihadist group.
"They were found in the living room of the house, in which they had moved about a month ago," the officer said on condition of anonymity.
Medical sources said some of the victims were found with their hands tied.
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"One of the sons was an officer in the former regime (of Saddam Hussein), three of the others are still students," the police colonel said.
Iraqi security forces are believed to be preparing a major offensive to retake Tikrit from IS, having reclaimed the entire province of Diyala earlier this year.
Tikrit is near the Speicher military base from which hundreds of new Iraqi recruits were kidnapped before being executed by the jihadists in the early days of their nationwide offensive in June last year.