"Four bodies recovered till now," the Indian navy said on Twitter, adding that a search for the remaining three was underway.
"Crash position indicator of ill-fated @ONGC_ helicopter recovered."
The navy posted photos of boat crews in helmets and life jackets scouring the waters where the debris was found.
The Indian Coast Guard said two of the four victims had been identified by the cards in their wallets, posting photos of an ONGC work ID and a driver's license.
The chopper was supposed to land at offshore oil rig Bombay High at 11:00 am, the Press Trust of India reported citing unnamed sources.
It was 40 nautical miles off the western coast before it went off-radar, the coast guard said.
"@indiannavy and @IndiaCoastGuard are extending all possible assistance in the #SAR Search and Rescue of @ONGC_ helicopter and pax on board. Wish for their safety," Nirmala Sitharaman, India's defense minister, said on Twitter.
The navy and coast guard dispatched ships, several boats and aircraft in search and rescue operations.
Civil Aviation Minister Jayant Sinha took to Twitter to express his anguish over the crash and said Indian air accident investigators would launch an inquiry into the matter.
ONGC said in a statement that "the reason behind the unfortunate incident is yet to be ascertained".
The helicopter had been leased to ONGC by the state-owned Pawan Hans helicopter firm, in which the oil producer holds 49 percent stake.
In 2015, a Pawan Hans chopper crashed after taking off from Bombay High, killing two pilots.
ONGC accounts for about two-thirds of the country's total natural gas production.
It made a significant discovery last year at Bombay High, India's biggest oil field, of reserves of about 20 million tonnes.
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