The embassy is seeking access to those under detention, Indian envoy in Kuwait Vidhu P Nair was quoted by the All India Radio as saying.
The embassy had managed to track down and collate documents of around 650 of them, he said.
All those with valid documents would be released, while the remaining might be deported to India, he said.
The Indians are among the more than 2,000 people who were arrested last week for expired visas and involvement in crimes during impromptu security checks.
Most of the arrested Indians are from the southern Rajasthan districts of Banswara, Pratapgarh and Dungarpur, reports Jaipur-based journalist Narayan Bareth.
The state’s Chief Minister Ashok Gehlot has written to External Affairs Minister SM Krishna asking him to help secure the release of the men.