The men wielding a knife and a machete stormed the police headquarters in North Sumatra's provincial capital of Medan and stabbed to death an officer who was at his post, said National Police spokesman Setyo Wasisto.
Responding officers shot the two attackers, killing one and seriously wounding the other, he said.
The attack came when most Indonesians were celebrating the first day of Eid al-Fitr holiday, which marks the end of the fasting month of Ramadan.
"They want to execute an IS command that tells their followers to carry out attacks anywhere with whatever they have," Wasisto told reporters in the capital, Jakarta.
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Indonesia, the world's most populous Muslim nation, has carried out a sustained crackdown on militants since the 2002 Bali bombings that killed 202 people, but a new threat has emerged from Islamic State group sympathizers. In recent years, smaller and less deadly strikes have been targeting the government, mainly police and anti-terrorism forces.
A twin suicide bombings last month killed three officers in the deadliest militant attack in Jakarta in a year. Police announced Thursday they have arrested 41 suspected militants following the bombing allegedly carried out by members of Jemaah Anshorut Daulah, which is affiliated with the IS group.
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