At least 10 Israeli nationals are trapped in buildings in India's financial capital Mumbai after attacks by militants, with a rabbi among a group being held hostage in an apartment building, officials said.

The Israelis have been caught up in a series of attacks in the city that have killed at least 119 people, police said.

"It could be 10 to 20, it could be more," said an official from the Israeli Embassy in New Delhi, who declined to be named. "I don't think it is less than 10."

Some, including the rabbi, were being held hostage by gunmen at Chabad House, where he and his wife ran a cafe and a synagogue for the Chabad Lubavitch religious group. The embassy official said between four and eight people were held there.

Others were trapped or held hostage at the nearby Trident-Oberoi Hotel, where Islamist militants were battling with elite Indian commandos.

At Chabad House, Indian commando Amit Tiwari told Reuters a woman and a child had been released, and one of the gunmen had been killed, but at least four armed men remained in the building.

The Israeli rescue service Zaka, an ultra-Orthodox organisation, identified the hostage as Rabbi Gabriel Holtzberg, but said his wife Rivka and a two-year-old child had been released.

"The situation at the present moment is very unclear. We know there is a hostage situation at the Chabad centre and also in one of the hotels in town," Foreign Ministry spokesman Yigal Palmore told Reuters Television earlier in the day.

Israel's Ynet Web site said other hostages, including the child's caregiver, were also released some time later. But it said the Holtzbergs were still being held.

Chabad Lubavitch said on its website that it was concerned about the welfare of Holtzberg and his wife.

"The Israeli Consulate was in touch with Holtzberg, but the line was cut in middle of the conversation," a report on the Chabad website said. "No further contact has since been established."

"It is not clear what the gunmen want," Tiwari said.