It was the second boat of asylum seekers the navy had pushed back since shortly before Christmas, police chief Hidayat said.
Indonesia's Foreign Minister Marty Natalegawa said the country opposed any moves by Australia to turn away asylum seekers.
"Let me just once again put on record our rejection of [policies] that resemble the pushing back the boat," he said. "Such policy is not actually conducive to a comprehensive solution to the issue."
The first boat, which originated from South Sulawesi, Indonesia and carried 47 people, was allegedly turned away Dec. 13. Indonesian authorities picked them up Dec. 19 from Rote Island. The second boat carried 45 people, the Australian Broadcasting Corp. reported Tuesday.