Paris (CNN) -- Nearly two years after an Air France plane mysteriously fell out of the sky, killing 228 people, the bulk of the wreckage has been found with bodies still aboard, French officials said Monday.

The human remains will be brought to the surface and identified, French Ecology and Transportation Minister Nathalie Kosciusko-Morizet said at a news conference.

Submarines searching for the wreck spotted two engines, the fuselage and landing gear over the weekend, officials said.

But the flight data recorders have not been recovered, leaving investigators as puzzled as ever about why the plane crashed in stormy weather on June 1, 2009.

"It's still a jigsaw puzzle," said Alain Bouillard, who will be in charge of the recovery operation. "We do not know where the recorders might be."

Kosciusko-Morizet said she was hopeful the flight data recorder, sometimes called the black box, would be found.

"The fact that we found various pieces, a lot of pieces of the plane in a quite concentrated area is a good hope for finding the black boxes, but we have no assurance," she said.

It is impossible to tell how many bodies remain in the wreck, he added. Fifty bodies were recovered in previous searches, leaving 178 victims still missing.

He would not comment on the condition of the bodies, calling it "inappropriate" to discuss.

The debris is dispersed over "quite a compact area" of about 600 meters by 200 meters (1,960 feet by about 650 feet), he said.

All the wreckage will be brought to the surface and sent to France for study, said Jean-Paul Troadec, head of the French air accident investigation agency, the Bureau d'Enquêtes et d'Analyses, or BEA.

"We want to know what happened in this accident, most particularly so it never happens again," he said.

Three companies bidding to raise the wreck have until Thursday afternoon to submit proposals, he said.

The operation should take three weeks to a month, and will be paid for by the French government at an estimated cost of 5 million euros ($7.1 million), he said.

Authorities are not revealing the exact location of the wreck to protect the site, officials said.

The head of Air France said the discovery was "good news indeed since it gives hope that information on the causes of the accident, so far unresolved, will be found."

Air France's Pierre-Henri Gourgeon added his thanks to the French authorities "who employed hitherto unheard of means to pursue searches."

Investigators announced Sunday that they had found pieces of the Airbus A330-200 that disappeared while flying to Paris from Rio de Janeiro.

After three unsuccessful searches, investigators discovered the wreckage by using "a different calculation based on currents of the sea and what might have happened," Troadec, the BEA chief, said Monday.

The BEA said Sunday that a team led by the Woods Hole Oceanographic Institution discovered parts during an underwater search operation conducted within the previous 24 hours.

Studies of the debris and bodies found after the crash led the BEA to conclude the plane hit the water belly first, essentially intact. Oxygen masks were not deployed, indicating that the cabin did not depressurize, the agency said in a 2009 report.

Automated messages sent from the plane in the minutes before the crash showed there were problems measuring air speed, investigators have said, though they said that alone was not enough to cause the disaster.

The area where the plane went down is far out in the Atlantic -- two to four days for ships to reach from the nearest ports in Brazil or Senegal in West Africa. The underwater terrain is rough, with underwater mountains and valleys, the BEA has said.