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The man identified as the father of the 29-year-old suspect in this week's deadly Christmas market attack in Strasbourg says his son subscribed to the beliefs of the Islamic State group.

The interview with Abdelkrim Chekatt by the state-run France 2 television channel was shown on Saturday night, two days after his son was tracked down and killed in a confrontation with three police officers.

"He'd say, for example, that Daesh, fights for the just cause and all that," Chekatt said, using an arabic abbreviation for the IS group.

The elder Chekatt added that he had in the past tried to dissuade his son, Cherif, from his extreme beliefs.

"You don't see the atrocities they commit," he recalled telling his son, who he said would deny that they had committed those acts.

Chekatt said he had seen his son three days before the attack but couldn't contact him while he was on the run.

He also said that if his son had told him about a project to kill "I would have denounced him, and he wouldn't have killed or been killed".

The interview, which began initially outdoors with the father, continued briefly inside with Cherif Chekatt's mother, Rouadja Rouag, who expressed shock and sorrow for the deaths. France 2 said the couple had been divorced for a long time.

Following the Tuesday night attack in which four people were killed and a dozen others were wounded, police detained and questioned the suspected shooter's father, mother and two siblings, among others. French media reported that the family members were released, however, three others who are unrelated to Chekatt are still in custody.

The father said he went to police of his own accord and on a suspicion the night of the son's rampage with a handgun and a knife.

He said he told police that "if ever you locate Cherif, tell me. I'll go to him and try to reason with him to give up".

The young Chekatt had been on a French intelligence watch list for radicalism and was convicted 27 times for criminal offences, the first time at age 13, mainly in France but also in Germany and Switzerland.

Investigators are trying to determine whether he had accomplices or logistical support.