A video distributed by the agency shows the Indonesian ship following the Chinese vessel on Friday afternoon.
China's coast guard said it was patrolling within its own jurisdiction.
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However, Indonesia's coast guard and navy insisted that the Indonesian Continental Shelf in the area has received international recognition and that Indonesia has sovereign rights to exploit and explore natural resources in that area without being disturbed by any country.
Indonesian authorities said the Chinese ship was first detected near survey vessel MV Geo Coral on Monday.Â
An Indonesian patrol ship contacted the ship, whose crew insisted that the area was under China's jurisdiction, before Indonesian coast guard and navy ships drove the Chinese ship away.
The second attempt happened on Wednesday morning when the Chinese ship again approached the site of a seismic survey and was driven away, according to the agency.
"Indonesia's Maritime Security Agency will continue to show its commitment to maintaining security and enforcing the law in Indonesian waters and Indonesian jurisdictional areas," said the statement from the agency.
China's "nine-dash line," which it uses to roughly demarcate its claim to most of the South China Sea, overlaps with a section of Indonesia's exclusive economic zone that extends from the Natuna Islands.
Indonesia does not have a formal territorial dispute with China over the South China Sea but has become increasingly protective of its rights in the region, while Chinese ships have regularly entered the area Indonesia calls the North Natuna Sea, fuelling tensions between the countries.
