Sheriff Rader could not say whether passengers were wearing life vests at the time of the capsizing, or if the boat's windows were open.
Patrol divers found two bodies on Friday, raising the initial death toll of 11 to 13, Pace said. Stone County Sheriff Doug Rader urged anyone with video or photos of the accident to contact authorities.
Two duck boats had been on the water at the time, according to Rader, one of which returned safely. He described the rescue effort as "outstanding".
Southern Stone County Fire Protection spokesman Eric Nielsen said he heard that more than 10 people were injured.
Schaumann said a severe thunderstorm warning was issued for Branson at 6:32 p.m. Thursday, before the boat tipped over.
Divers have been searching the lake for about five others who are missing.
"This incident has deeply affected all of us", Smagala-Potts said. "My deepest sympathies to the families and friends of those involved in the awful boat accident which just took place in Missouri". He wrote Friday on Twitter, "Such a tragedy, such a great loss".
Nicc Hippy wrote, "I believe once the boat capsized they were trapped".
Table Rock Lake, east of Branson, was created in the late 1950s when the Corps of Army Engineers built a dam across the White River to provide hydroelectric power to the Ozarks.
"We got one of the life carriers, one of those things we got her in there and pulled her up, and I was yelling for people to get CPR", said Behr. "Oh my God, those poor people, oh no!" someone says in the background as the water appears to swallow the bopping boats.
Rader said 31 people were on board the boat, including children.
A spokesman with the Missouri Highway Patrol said the age range of those who died was from 1 to 70 years old, according to AP.
Branson is about 200 miles south east of Kansas City and is a popular vacation spot for families and other tourists looking for entertainment ranging from theme parks to live music.
On Friday morning, Missouri Governor Mike Parson said of the tragic situation, "Our thoughts and prayers right now are with these family members".
At the time, he said, the lake seemed calm, and no one was anxious about the weather. Team will travel Friday morning.
National Weather Service meteorologist Steve Linderberg told the Springfield News-Leader newspaper that winds reaching 63 miles (101 km) per hour were recorded at the Branson airport near the time of the incident.
A spokeswoman for the Cox Medical Centre Branson said four adults and three children arrived at the hospital shortly after the incident.
Seven people have been hospitalized, he said, and a local hospital said two were in critical condition.
The storm was part of a larger batch of severe weather that battered many parts of the United States on Thursday, from Minnesota to Arkansas. The National Weather Service had issued a severe thunderstorm warning for the area during the period the boat sank.