Eight navy ships and sonar systems had joined the search for victims of Wednesday's incident, along with 20 civilian boats in stormy weather off the southern coast, the military said.
"We have not received any information about survivors," said Phyu Phyu Win, a regional social welfare and relief official. "Hopefully someone would survive."
Scores of soldiers gathered on standby to assist if more bodies were carried ashore in the fishing village of Sanlan, about 600 km (372 miles) from Myanmar's largest city Yangon.
Twenty-three adults and eight children made up the tally of bodies pulled from the Andaman Sea near the coastal town of Launglon since rescue efforts began on Wednesday, the military said on its official page on social media site Facebook.
Soldiers, family members and crew were on board when the weekly flight, from several coastal towns to Yangon, went missing.
The Chinese-made Y-8-200F transport plane lost contact 29 minutes after takeoff, while at a height of 18,000 feet (5,485 metres) over the Andaman Sea, about 43 miles (70 km) west of the town of Dawei, the military said.
An aircraft wheel, two life jackets and some bags with clothes - believed to be from the missing plane - were found on Thursday. Some patches of oil were also spotted, the military said.
The cause of the incident is yet to be confirmed.
Survivors are unlikely more than 24 hours after the plane lost contact, despite warm sea temperatures, experts have said.
Many bodies had fragmented into several pieces and no victim wearing a life jacket has yet been recovered, said a member of the emergency team.
Aircraft accidents, involving both civilian and military planes, are not uncommon in Myanmar.
A military helicopter crashed last June in central Myanmar, killing three military personnel. Five were killed in February last year when an air force aircraft crashed in the capital, Naypyitaw, media said.
(Reporting by Wa Lone, Yimou Lee and Aye Win Myint; Editing by Clarence Fernandez)
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