Families had to endure an agonising wait for news
Indonesian officials have confirmed that bodies and debris found in the Java Sea off Borneo are from AirAsia flight QZ8501 that went missing on Sunday, a statement by AirAsia says.
AirAsia CEO Tony Fernandes said he was "devastated" by the news.
President Joko Widodo told media he had instructed all search teams to focus on finding the passengers and crew.
The Airbus A320-200, carrying 162 people from Surabaya in Indonesia to Singapore, disappeared on Sunday.
The navy said 40 bodies have been recovered, though other officials have given much smaller figures.
The discovery came on the third day of searching. A navy spokesman said rescuers were "very busy now" with the salvage operation.
'Families are priority'
The AirAsia statement said the remains were found in the Karimata Strait, south west of Pangkalan Bun in the Borneo province of Central Kalimantan.
Mr Fernandes said: "I am absolutely devastated. This is a very difficult moment for all of us at AirAsia as we await further developments of the search and rescue operations but our first priority now is the wellbeing of the family members of those on board QZ8501."
The statement said family members would be assigned care providers and an emergency call centre set up for those seeking information.
The pilot's wife (pictured right, with headscarf) was among those waiting for news at Surabaya airport
Searchers have found what they think is the missing plane's slide
Pictures of debris were taken by search and rescue aircraft
In a news conference shortly after the discovery was confirmed, Mr Widodo urged relatives to be strong in facing "this difficult moment".
"I have instructed all the teams to focus on finding the passengers and crew," he said.
The first debris from the plane was spotted earlier on Tuesday. Pictures of debris and bodies were shown on Indonesian TV. Relatives of passengers on the plane watching the pictures were visibly shocked.
At the scene: Alice Budisatrijo, BBC News, Surabaya airport
They had been hoping for a miracle, but in the end they had to watch the worst possible news.
Relatives of the passengers screamed and wailed as local television networks showed pictures of what was clearly a human body floating in the water.
Grown men put their hands to their faces. At least two people collapsed and were taken out of the room on stretchers.
The mayor of Surabaya, Tri Rismaharini, went from one crying relative to another, and at one point walked out with a grieving man, while telling him: "We don't have a choice. Today this happens to you, tomorrow it may happen to me. Nobody knows. So you have to be strong. Our lives belong to God."
It's been a trying and exhausting wait for the more than 100 relatives who have been gathering in that room, but no-one could have been prepared for this ending.
The head of the search operation, Bambang Soelistyo, said that a shadow was also spotted under the water, which appeared to be in the shape of a plane.
All resources were now being sent to the area where the debris was found, he said.
Mr Soelistyo added that ships with more sophisticated technology were being deployed to check whether larger parts of the plane were submerged beneath the debris.
AFP journalist Bay Ismoyo, who took some of the first photos of the debris, said he saw "an orange object floating on the waters".
"We saw an unusual object floating. We tried to zoom in and we recognised what looks like a life vest."
At least 30 ships, 15 aircraft and seven helicopters joined the operation when it resumed at 06:00 local time on Tuesday (23:00 GMT Monday).
The operation, led by Indonesia, includes assistance from Malaysia, Singapore and Australia, with other offers of help from South Korea, Thailand, China and France. The US destroyer USS Sampson is on its way to the zone.
On board the plane were 137 adult passengers, 17 children and one infant, along with two pilots and five crew.
Most were Indonesian but the passengers included one UK national, a Malaysian, a Singaporean and three South Koreans.
AirAsia previously had an excellent safety record and there were no fatal accidents involving its aircraft.