Suddenly the militants exited the auto and immediately stage strikes with swords against policemen, provincial police spokesman Sunarto said.
The group slammed a minivan into a gate and then attacked officers with swords.
The attack is the latest in a spate of attacks in the country.
Separately, Sunarto said police are still searching for more attackers.
"Four of them got out of the auto 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.
The Sunday attacks were followed by another suicide bombing involving a family, this time on a Surabaya police station.
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A day later, a family of five carried out a suicide bombing attack on a police headquarters in Surabaya that left 10 people wounded, including four policemen and six civilians.
The National Police's elite antiterrorism squad, Detachment 88, has captured several suspected terrorists in East Java, North Sumatra and South Sumatra following the incidents in Surabaya and Sidoarjo.
All six bombers were killed, including the mother who was Indonesia's first known female suicide bomber.
The coordinated church attack was a sign local extremist groups were becoming more proficient, and stirs concerns about an uptick in extremism as hundreds of Indonesians who flocked to fight alongside Islamic State in the Middle East return home. Gen. Setyo Wasisto said in a press briefing in Jakarta.
One local journalist at the scene sustained minor injuries in the attack, police said.