Justices Abhay Oka and Anil Menon asked ACB to file its report by March 20, adjourning the hearing to March 24.
V R Musale, an activist, has filed a petition seeking prosecution of Gavit and his family.
As ACB asked for two months to complete the open inquiry, Musale's lawyer Uday Warunjikar objected, saying that enough time had already been given. However, the court decided to give the agency some more time.
At an earlier hearing, the High Court had pulled up ACB for delay in completing the open inquiry.
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Income Tax Department has reopened the assessment of incomes and assets of Gavit and his relatives from 2007-08.
ACB had earlier held a 'discreet inquiry' into the assets of Gavit and his family members and said it had found material against them. On March 5, it sought the erstwhile Congress-NCP government's permission to start an open inquiry.