"Aerial spraying of chemicals to contain the spill is going on. But oil is still leaking from the cargo and it is likely the slick will spread further because of the tide and windy conditions," Nambiar said.
Environmental emergency teams have been put on alert to mobilise for a clean-up operation, while fishermen have been told not to venture into the sea until the all-clear has been given.
Nambiar described the ship's position as "precarious", adding that "it's difficult to get on board to locate the point of leakage".
Six coast guard ships were working to minimise the impact of the spill.
Broken patches of oil have been cleared around Elephanta Island, a world heritage site and tourist attraction in Mumbai Harbour, the defence ministry said in a statement.
The MSC Chitra was leaving Mumbai when it collided with the MV Khalijia-II, which was manoeuvring into port.
Thirty-three crew members were rescued. Both ships developed cracks following the collision.