Maharashtra Chief Minister also resign
Vilasrao Deshmukh said he was awaiting a Congress party decision. His deputy, RR Patil, has already resigned.
Correspondents say there are calls for more resignations amid questions over whether all the gunmen have been found.
Attackers with guns and bombs targeted multiple locations from Wednesday, killing at least 172 people.
On Monday, Mumbai began to return to normal with markets and schools open and heavy traffic on the streets.
