Rescue teams working through the night recovered many bodies as well as the jet's flight recorder, officials said.
The Bhoja Air Boeing 737, which had flown from Karachi, crashed on its approach to the airport during a storm.
Grieving relatives of the victims have been gathering at airports in Karachi and Islamabad.
The head of Bhoja Air has been barred from leaving the country pending the outcome of the inquiry, officials said.
The wreckage of the plane has fallen over a number of kilometres but much is concentrated over the small village of Hussain Abad. We still don't know if any villagers have become casualties.
Body parts are spread all over the place - in nearby fields, inside the village, in front of houses, and in the narrow streets. You can see bits of clothing and belongings scattered all over the place.
Rescuers are now trying to collect the body parts and put them into body bags to secure them and take them to hospital. They will eventually help with identification.
The plane came down in the village of Hussain Abad on the outskirts of Islamabad on Friday evening, scattering debris over a wide area. There are so far no reports of villagers being among the casualties.
Pakistani official Capt Arshad Mahmood said there was a heavy thunderstorm with hail as the plane came in to land.
"The weather was very bad. The pilot lost control and hit the ground. It [the plane] tossed up due to the impact and exploded and came down in a fireball," he said.
The BBC's Aleem Maqbool in Islamabad says some people have also called into question the age of the aircraft and Pakistan's system of regulating air safety.
Interior Minister Rehman Malik said that Farooq Bhoja, head of Bhoja Air, had been barred from leaving the country as the investigation gets under way.
"It is being said that the aircraft was pretty old, so it has been ordered to investigate thoroughly the air worthiness of the Bhoja Air aircraft," Mr Malik said.
"The causes will be investigated, whether it was any fault in the aircraft, it was lightning, the bad weather or any other factor that caused the loss of precious lives."
The victims are said to include 11 children and a newly married couple.
A Bhoja Air official in Karachi said it was making arrangements to fly one member from each family to the capital.
At Islamabad airport, one man yelled "my two daughters are dead", before slumping to the floor in a state of shock.
The uncle of the sisters, aged 18 and 20, said: "We don't even know when or where we will get to see their bodies."
Bhoja Air is a small commercial airline that started domestic flights in 1993. It suspended operations in 2001 because of financial difficulties but recently re-opened.
In July 2010, an Airblue Airbus A321 crashed as it was about to land in Islamabad, killing all 152 people on board - Pakistan's worst-ever air disaster.
Although Pakistan's air industry has been booming, critics say standards have not always kept pace with the increase in services.
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