The Azerbaijan state oil company (SOCAR) says rescue efforts have been hampered by high winds and choppy seas but that 29 employees are now safe on land.
Fire broke out Friday afternoon on an offshore oil platform operating in the deep water Guneshli section of the Azeri-Chiraq-Guneshli oil field in the south Caspian Sea.
The company released a statement that said the fire continues to burn on Saturday.
There has been no official information about casualties or how many workers might still be on the platform. Earlier the firm said many were taking refuge on life boats attached to the platform.
But the Azerbaijan Oil Workers' Rights Protection Committee - an independent watchdog - has claimed many fatalities.
"According to our information, 32 workers died, while 42 workers were rescued last night. ... The fire on the platform was finally extinguished," Mirvari Gakhramanly, the group's head, told the Reuters news agency.
In addition, one oil worker contacted a Reuters correspondent from the platform and said 84 people were trapped aboard. The worker did not want to be named.
SOCAR has declined to respond to these reports.
About 60 percent of SOCAR's oil production passes via the platform where the fire broke out, meaning the company's output will certainly be affected.
Fourteen workers were reported killed in accidents on SOCAR's oil and gas platforms in 2014.
jar/jlw (AP, Reuters)