The bodies of three crew members, trapped inside the cabin, had been found, the Department of National Defence Search and Rescue told dpa on Sunday.
Among the confirmed dead are eight children.
The boat, carrying 48 tourists and five crew members, capsized about 2pm on Saturday as Storm Wipha approached the country across the South China Sea.
Vietnamese Prime Minister Pham Minh Chinh urged authorities to prioritise rescue operations.
Authorities mobilised 323 personnel for the rescue operation, including border guards, the navy, police and port authorities.
Halong Bay, a UNESCO World Heritage Site, spans over 1500sq/km and is dotted with nearly 2000 islands and islets.
It is one of Vietnam's most popular tourist destinations, attracting millions of visitors each year.
Most of the tourists were from the capital Hanoi, local newspaper VnExpress reported.Rescue teams found 11 survivors, the state-run Vietnam News Agency said citing local authorities.
A 14-year-old boy was reportedly among the survivors, and he was rescued four hours after being trapped in the overturned hull.
Storm Wipha, the third typhoon to hit the South China Sea this year, is projected to make landfall along Vietnam's northern coast early next week.
Weather linked to the storm also disrupted air travel.
Noi Bai Airport said nine arriving flights were diverted to other airports and three departing flights were temporarily grounded on Saturday.
with Reuters and dpa
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