A plane was burning in the air before it plummeted to the ground shortly after take-off in Pakistan, according to witnesses.

The plane went missing in the country's north with 48 people on board and officials have said they do not expect to find any survivors.

"The way the plane crashed and broke into pieces, there is no chance of any survival," Sardar Aurangzeb Nalota, a local legislator, said.

"The fuel tank is still on fire, the plane debris is scattered in the mountains and residents told me that it is completely destroyed."

Pakistani TV channels reported that flight PK-661 took off from the city of Chitral but lost contact with ground control shortly afterwards.

The aircraft, operated by Pakistan International Airlines (PIA) crashed around 4.50pm local time, in the Havelian area of Khyber Pakhtunkhwa province.

It was flying to the country's capital, Islamabad, when it hit a mountain slope.

Taj Muhammad Khan, a government official based in the Havelian region, told Reuters: "All of the bodies are burned beyond recognition. The debris is scattered."

The army said 21 bodies had been recovered so far.

Villagers were reportedly collecting body parts in shawls and on woven beds at the site, which is only accessible on foot.

It is believed Pakistani popstar Junaid Jamshed, whose Dil Dil Pakistan was an unofficial anthem, was believed to be among the dead. The singer turned evangelical Muslim had been in Chitral.

Forty of those on board were passengers and eight believed to be crew.

Irfan Elahi, the government's aviation secretary, told media the ATR-42 turboprop aircraft suffered engine problems but it was too early to determine the cause of the accident.

Pakistan's deadliest crash was in 2010, when an Airbus 321 operated by private airline Airblue and flying from Karachi crashed into hills outside Islamabad while about to land, killing all 152 on board.