The Indonesian president has ordered a full investigation into the crash and there have been calls for the country's transport minister to resign.
Some government officials hinted that sabotage will be investigated as a possible cause of the crash.
Andi Mallarangeng, a government spokesman, said investigators would look into possible "non-technical" causes.
Early reports said that the tyres of the aircraft, a Boeing 737-400, were responsible for the crash.
"Some witnesses said that the tyres burst on land, others said that they saw flames as the plane came into land," said Dan Nolan, an Al Jazeera correspondent in Yogyakarta.
The aircraft was carrying seven crew and 133 passengers; witnesses said it took firefighters two hours to extinguish the blaze.
Wayan Sukaro, a cameraman who was on the plane to cover an official visit to Indonesia by Alexander Downer, Australia's foreign minister, described what happened.
Sukaro said: "The flight was on schedule but ten minutes before touchdown the pilot did not appear to be in control when he began to descend.
"There was hysteria everywhere. We felt like we were being hit by turbulence. There was panic everywhere.
"As we were landing I saw the aircraft tyres coming out. There was a large bang as the plane hit the ground.
"The aircraft was out of control. It overan the runway. The luggage in the cabin was falling on the passengers. The plane came to a stop, there was pandemonium all around.
"The cabin crew told us to get out. I jumped out and was injured in the leg. I then started running, I ran to get away as I was afraid of the plane exploding.
"Then I am alive, this may be god's miracle, I believe that."
Feb 22 2007: About 50 people die in a fire on the Levina 1 ferry travelling between Jakarta and the island of Bangka
Jan 16 2007: Five killed, 100 injured in train derailment near Purwokerto, central Java
Jan 1 2007: An Adam Air Boeing 737 with 102 passengers and crew disappears near Polewali in Sulawesi.
Dec 30 2006: More than 400 people thought to have drowned when the Senopati Nusantara ferry sinks during a storm in the Java Sea
Apr 15 2006: 26 killed and 13 injured in collision between two trains on Java
Sep 5 2005: About 150 people die when a Mandala Airlines Boeing 737 crashes into houses on take off from Medan in north Sumatra
The Australian government has said it believes up to 10 of its citizens were on board, including several journalists. Only five are known to have survived.
"We should be prepared for bad news in relation to at least some of the Australians on board the aircraft," John Howard, the Australian prime minister, told a news conference.
"It is a terrible tragedy. Many lives have been lost and our love and sympathy and condolences go to those who are suffering distress and grief."
Howard said there was no evidence that the crash was anything other than an accident.
"I have not received any advice suggesting it was anything other than a tragic accident," he said.
"I've not receive any advice suggesting that there was sabotage or a terrorist attack."
Indonesia, the world's most populous Muslim country, has been the scene of several bloody attacks on Australian tourists.
String of disasters
Indonesia has been hit by a series of air disasters in recent years.
On 1 January, a passenger plane operated by budget airline Adam Air crashed into the ocean, killing all 102 people on board.
In September 2005 about 150 people died when a Mandala Airlines Boeing 737 crashed into houses on take off from Medan in north Sumatra
Following the Adam Air crash, the government said it was looking at banning local commercial airlines from operating planes more than 10 years old.
However, most experts say proper maintenance and the number of takeoffs and landings are the critical factors in preventing accidents.
A number of Australian journalists and officials were on board, on their way to join the visit by Downer.
The minister himself was not on board, and Austrlia's prime minister, John Howard, has offered assistance:
"I've given authority for any aircraft, medical assistance and the like that is needed not only for the Australians but for others involved in the accident to be made available immediately," he said.