A magnitude 7.7 quake struck in the Gorontalo area of Sulawesi island at a shallow depth of 10 km (6.2 miles), the agency said.
It said a second 6.0 magnitude quake struck shortly afterwards in northern Sulawesi.
The U.S. Geological Survey said the second quake, at 1734 GMT, was 5.6 magnitude at a depth of 9.9 km (6.2 miles), 83 miles northwest of Gorontalo.
Indonesia launched a new hi-tech system on Tuesday aimed at detecting a potential tsunami and providing faster alerts in a region battered by frequent earthquakes.
The sprawling archipelago of some 17,000 islands, which lies in the seismically-active "Pacific Ring of Fire", was hit by a devastating tsunami four years ago that left an estimated 170,000 people dead or missing in Aceh province.
(Reporting by Telly Nathalia, Writing by Ed Davies; Editing by Janet Lawrence)
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