Officials tell Eyewitness News one of those victims was found dead Saturday night, and crews were still working to find the second man.
Coast Guard officials said in a news release Saturday that helicopters were searching for the missing workers from the air, while a cutter searched the sea.
Chief Petty Officer Bobby Nash told The Associated Press that the search was ended at about 5:25 p.m. CST.
It was at that time that a dive team hired by the owner of the platform, Houston-based Black Elk Energy, located the victim's body. That team continued their search Saturday night.
The victim was only identified as a contract worker from oilfield contractor Grand Isle Shipyard. Grand Isle Shipyard employed 14 of the 22 workers on the platform at the time of the incident. A man who answered the phone at the company's Galliano, La., office on Saturday said no one was available to comment.
Black Elk Energy officials said the victim's body remained on the sea floor Saturday night. Crews were working to recover it.
The blaze, which started Friday, severely burned at least four workers. Their burns were not as extensive as initially reported, said Leslie Hoffman, a spokeswoman for Black Elk Energy.
Officials at Baton Rouge General Medical Center said Saturday that all four burn victims are in critical, but stable condition. They are awake but not communicating. All four are employees of Grand Isle Shipyard and are from the Philippines. The hospital said it and Grand Isle Shipyard are trying to reach the men's families in the Philippines.
Officials are still investigating what started the fire, but they have now ruled out a cutting torch, which they previously blamed.
Meanwhile, officials said no oil was leaking from the charred platform, a relief for Gulf Coast residents still weary two years after the BP oil spill illustrated the risk that offshore drilling poses to the region's ecosystem and economy.
The images Friday were eerily similar to the Deepwater Horizon blaze that killed 11 workers and led to an oil spill that took months to bring under control. The fire came a day after BP PLC agreed to plead guilty to a raft of charges in the 2010 spill and pay a record $4.5 billion in penalties.
There were a few important differences between this latest blaze and the one that touched off the worst offshore spill in U.S. history: Friday's fire at an oil platform about 25 miles (40 kilometers) southeast of Grand Isle, Louisiana, was put out within hours, while the Deepwater Horizon burned for more than a day, collapsed and sank.
The site of Friday's blaze is a production platform in shallow water, rather than an exploratory drilling rig like the Deepwater Horizon looking for new oil on the seafloor almost a mile (1.6 kilometers) deep.
The depth of the 2010 well blow-out proved to be a major challenge in bringing the disaster under control.
The Black Elk platform is in 56 feet (17 meters) of water -- a depth much easier for engineers to manage if a spill had happened.
A sheen of oil about a half-mile (800 meters) long and 200 yards (180 meters) wide was reported on the Gulf surface, but officials believe it came from residual oil on the platform.
"It's not going to be an uncontrolled discharge from everything we're getting right now," Coast Guard Capt. Ed Cubanski said.
Hoffman said Saturday that there were still no signs of any leak or spill at the platform site.
BP's blown-out well spewed millions of gallons (liters) of oil into the sea, about 50 miles (80 kilometers) southeast of the mouth of the Mississippi River on the east side of the river delta. The crude fouled beaches, marshes and rich seafood grounds.
After Friday's blaze, 11 people were taken by helicopter to area hospitals or for treatment on shore by emergency medical workers.
The production platform is on the western side of the Mississippi River delta. The Coast Guard said 24 people were aboard the platform at the time of the fire.
Cubanski said the platform appeared to be structurally sound. He said only about 28 gallons (106 liters) of oil were in the broken line on the platform.
David Smith, a spokesman for the Interior Department's Bureau of Safety and Environmental Enforcement in Washington, said an environmental enforcement team was dispatched from a Gulf Coast base by helicopter soon after the Coast Guard was notified of the emergency. Smith said the team would scan for any evidence of oil spilling and investigate the cause of the explosion.
Black Elk is an independent oil and gas company. The company's website says it holds interests in properties in Texas and Louisiana waters, including 854 wells on 155 platforms.
John Hoffman, Black Elk's president and CEO, went to Louisiana Saturday morning to assist in the investigation and help the families of the missing and injured workers.
"My entire focus is the families and workers. Nothing else matters at this point," he said.
Please stay with Eyewitness News and abc13.com for updates as we continue following this developing story. ABC13 reporter Miya Shay is in Louisiana to bring you the latest details on the search for the two missing workers and the aftermath of the explosion. Follow her on Facebook and Twitter for additional information.