In his weekly radio program today, Brazil's president Luiz Inácio Lula da Silva said, "We will do whatever is within our reach, together with the Air Force and the Navy, to find everything we possibly can. And, above all, the bodies, because in this moment of grief, even though that will not solve the problem, it will be immensely comforting to the families to know that they are burying their loved ones."
The hunt for the plane's black boxes also begins in earnest this week.
Today, the U.S. Navy sends a team and two underwater, high-tech listening devices used in military crashes. The devices are towed behind a boat to listen for the "pinging" signal emitted from the plane's cockpit voice recorder and flight data recorders. They can detect the black boxes at depths of 20,000 feet and have been used in military accidents.
A French nuclear submarine is expected to arrive Wednesday to look for the black boxes. Those recorders could also tell investigators whether the pilots tried to turn back toward land. Investigators believe may have been the case, based on the location of the wreckage and bodies.
"The black boxes are really going to give a lot of information, a good 90 percent of the information," Ciaccio said. "These are all pieces of the puzzle. It would be like an incomplete puzzle with the black boxes not being recovered."
The boxes' locator signals may last just 22 more days.
A total of 16 bodies recovered so far -- two Saturday and 14 Sunday -- give searchers a clearer idea of where plane went down. So do hundreds of personal items, including a piece of luggage and a boarding pass for the flight, as well as pieces of the plane found over the weekend.
Also this weekend, French investigators revealed that the plane sent out 24 electronic messages in four minutes detailing problems with electrical systems, pressurization and speed sensors.
"It does appear this air data system was involved in some way," said John Hansman, professor of aeronautics at the Massachusetts Institute of Technology. "They have to figure out why it went bad."
But experts caution about jumping to conclusions. The tragic accident was likely not caused by just one single failure, but rather a series of mishaps that brought the plane down.
"Airplanes are designed with sufficient redundancy that a single failure shouldn't cause an accident," Hansman said.
ABC News' Zoe Magee, Ammu Kannampilly, Renata Araujo, Sonia Gallego, Joe Goldman, Christel Kucharz, Luis Martinez, Phoebe Natanson, Fabiola Antezana, Gabriel O'Rorke, Samira Parkinson-Smith, Kirit Radia and Christophe Schpoliansky, Reuters and The Associated Press contributed to this report.