The Special Investigation Team (SIT) had earlier summoned Kamat, a sitting MLA, for questioning today.
Superintendent of Police (Crime Branch) Karthik Kashyap today said the SIT received a letter from Kamat seeking time till Friday to appear before the investigating officer, owing to ill health.
The former chief minister would be summoned again on Friday for the interrogation, Kashyap said.
The district court yesterday granted interim anticipatory bail Kamat in connection with the illegal mining scam case.
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The SIT is investigating Kamat's role in a case filed in September 2014 against mine owner Prafulla Hede.
It has been alleged that the delay in the renewal of the lease for a mine at Collem in South Goa was condoned by the government in an irregular manner when Kamat was holding mining portfolio.
Justice M B Shah Commission, which probed the alleged rampant illegal mining in Goa, had observed in its report that several mining companies were allowed to fraudulently use the provision of condoning the delay in renewal of mining lease.
The SIT has questioned several officials, including former principal mines secretary of the state Rajiv Yaduvanshi.