"Four of them got out of the vehicle and tried to fight a group of police with samurai swords", Nandan, who uses only one name, said in a live interview with local television station TV One.
Three militants were killed and one injured when eight terrorists attacked a police headquarters in Indonesia's Riau province on Wednesday, police said.
The driver of the van then attempted to the flee the scene, hitting and killing one police officer, he added.
Riau Police Chief Inspector General Nandan said a group of suspected militants crashed a auto into the gate of the headquarters around 9 a.m.
A footage showed that a man lying on the ground with a sword next to his body.
Indonesian media said one attacker may have had a bomb strapped to his body but police did not immediately confirm the reports.
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The Sunday attacks were followed by another suicide bombing involving a family, this time on a Surabaya police station. All three incidents involved the children of the three families, who knew each other and studied the Quran together, police said Tuesday.
"Four suspects were killed by police personnel during the attack".
Islamic State has claimed responsibility for both attacks.
This week's bloody violence is putting pressure on lawmakers to pass a stalled security law that would give police more power to take pre-emptive action against people suspected of planning terror attacks.
The church bombing family were in the same religious study group as the two other families linked to the attacks, police said.
They are now pursuing a militant who had escaped.