"All Tanzanians are with you in mourning the 19 people who lost lives during this accident," Majaliwa told a crowd after arriving at Bukoba airport, where the flight had been scheduled to land from financial capital Dar es Salaam.
It was not immediately clear if the 19 victims included rescuers who drowned or whether the 48-seater aircraft had more people on board than previously disclosed, a regional official said.
Regional authorities and the airline earlier said that 26 survivors out of the 43 people on board flight PW 494 had been pulled to safety and taken to hospital in the lakeside city in Kagera region.
"We are continuing to investigate, there is a possibility that two people were not onboard but died during the rescue effort," said Kagera regional commissioner Albert Chalamila.
"An investigation team consisting of Precision Air technical staff and TAA (Tanzania Airports Authority) has also departed to join the rescue team on the ground," the airline said in a statement.
Precision Air, a publicly listed company which is Tanzania's largest private airline, said it had dispatched rescuers to the scene.
"Precision Air sincerely understands the anxiety for confirmed information and will therefore do its best to issue more details," the company said.
Video footage broadcast on local media showed the plane largely submerged as rescuers, including fishermen, waded through water to bring people to safety.
Emergency workers attempted to lift the aircraft out of the water using ropes, assisted by cranes as residents also sought to help.
President Samia Suluhu Hassan expressed her condolences to those affected by the accident.
"Let's continue to be calm while the rescue operation continues as we pray to God to help us," she said on Twitter.
The African Union Commission chair Moussa Faki Mahamat also shared his condolences, as did the secretary general of the regional East African Community bloc, Peter Mathuki.
Precision Air, which is partly owned by Kenya Airways, was founded in 1993 and operates domestic and regional flights as well as private charters to popular tourist destinations.