Jakarta also pledged to step up maritime patrols in areas where it fears its "territorial integrity" could be violated.
It came after the Australian government apologised unreservedly to Jakarta after its navy "inadvertently" violated Indonesian waters during border security operations.
"The government of Indonesia deplores and rejects the violation of its sovereignty and territorial integrity by Australian vessels," said a statement from the Indonesian ministry for security, political and legal affairs.
"The government of Indonesia underlines that any such violations... Constitute a serious matter in bilateral relations of the two countries."
The statement, read to reporters by ministry spokesman Agus Barnas, demanded a halt to Australia's military-led Operation Sovereign Borders until assurances are received there will not be a repeat of such violations.
"Indonesia demands that such operations conducted by the Australian government that led to this incident be suspended until further clarification is received," the statement said.
"Indonesia for its part will intensify its maritime patrols in areas where violations of its sovereignty and territorial integrity are at risk."
Barnas said that the Indonesian navy would send an extra ship to patrol its southern maritime borders around the island of Timor.
Despite its navy boats having violated Indonesian waters, Canberra has vowed to pursue its hardline policies.
The Indonesian government statement was issued after a meeting between the security ministry, the foreign ministry, police and military.
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