"We deeply regret the loss of tens of lives in the boat accidents in Para and Bahia," two states in the north of the country, President Michel Temer said on Twitter.
Regional authorities in north-central Para state said 21 people were confirmed dead so far after a boat sank on the Xingu river late on Tuesday.
That vessel, the Capitan Ribeiro, had 49 people on board, 23 of whom were rescued.
Emergency teams were still searching for five more, the department said in a statement.
Separately, the navy said 18 people died when a ferry sank early Thursday off the northeastern state of Bahia.
Naval commander Flavio Almeida lowered the death toll in that accident from an earlier count of 22.
That boat reportedly had at least 120 people on board. Almeida said at least 21 of them had been rescued by official means, but he added that many more were believed to have been picked up by civilian vessels.
The boat was running the short route from the island of Itaparica across the bay to the city of Salvador, capital of Bahia state, when it went down in a storm.
"It was raining... a wave came and the boat turned over. There were a lot of people" on board, one survivor, Edvaldo Santos de Almeida, told top news website G1.
The naval commander said scores of military personnel were working on rescue efforts at the site.
The state government declared three days of mourning.
"I have been personally following this difficult operation from an early stage and all measures have been taken immediately," said Bahia governor Rui Costa.
Search for survivors
In the incident in Para, in a northern Amazon region, survivors told local media that the boat got caught in a rainstorm.
The vessel had left the port of Santarem bound for Vitoria de Xingu. The regional public safety department said 21 people were confirmed to have died in that sinking, including two children.
Rescuers were searching for others missing in the Xingu river.
"It’s a hard-to-access area," Colonel Augusto Lima, from the Para firefighters’ service, was quoted as saying on Wednesday by the newspaper Folha de Sao Paulo.
The victims who were rescued got out by swimming, Globo news reported, saying the boat went down about 500m from the riverbank.
Ferries, fishing vessels and big commercial ships ply the Amazon waterways as one of the main forms of transport in a region with relatively few roads.
Some 1,160 people have been killed in accidents on rivers in the Amazon since 1981, according to Folha, source from Vietnamnews.