Sixty-one Dutch nationals were among those killed, Dutch tourism board ANWB said. A Dutch boy was the sole known survivor, the Libyans say.
British and South African passengers are also thought to have been on board. The 11 crew were said to be Libyan.
Nicky Knapp, a spokeswoman for Airports Company South Africa, said seven passengers were booked to connect to London Gatwick airport, 32 to Brussels, 42 to Dusseldorf in Germany, and one to Charles de Gaulle in Paris.
"Nationalities and names won't be revealed at this stage," she said.
"A 24-hour helpline has been set up to assist families and relatives."
Dutch Prime Minister Jan Peter Balkenende confirmed that "several dozen" Dutch nationals were killed.
Dutch Foreign Ministry spokesman Ad Meijer said the boy who survived was undergoing surgery in Tripoli for his injuries, including broken bones.
Afriqiyah Airways said on its website: "We are very sorry to announce the tragic loss of Afriqiyah Airways flight 8U771 from Johannesburg in an accident during landing at Tripoli International Airport at 04:00 UTC (06:00 am Tripoli time) today Wednesday 12 May.
"We extend our deepest sympathy to the families and friends of the victims. The search and rescue mission has now been completed."
Libyan Transport Minister Mohammed Ali Zidan said 104 people had been on board the plane - 93 passengers and 11 crew.
He said that the remains of 96 victims had already been recovered.
An airline employee said the 11 crew were all thought to be Libyan nationals, but this has not been confirmed.
Britain's Foreign and Commonwealth Office said said it was "aware of reports that there were British nationals on board the flight, but this has not been confirmed".
"We are urgently investigating. A consular team from the British Embassy are on their way to the airport. Consular staff in Tripoli are urgently seeking further details," it said.
Libya's state TV showed footage of a field scattered with pieces of plane debris, and police and rescuers walking with surgical masks and gloves.
The cause of the crash was not immediately known. Some reports suggest the plane crashed very close to the runway.
"It exploded on landing and totally disintegrated," a Libyan security official told news agency AFP.
A flight recorder has already been recovered, and officials hope this will provide some clues as to what caused the disaster.
However, Mr Zidan ruled out terrorism as the cause of the crash.
The airport is currently sealed off and ambulances have been going back and forth to the airport.
Our correspondent adds that the weather has been sunny and clear over the past few days.
Afriqiyah Airways is a low-cost Libyan airline founded nine years ago and operates a relatively new fleet of Airbus aircraft.
It flies many routes between Africa and Europe with passengers often transiting through Tripoli, our correspondent adds.
Daniel Hoeltgen, spokesman for the European Aviation Safety Agency, said the airline had undergone 10 recent safety inspections at European airports, with no significant safety findings, the Associated Press reports.
He added that a team of French crash investigators was already on its way to Tripoli to help Libyan officials determine the cause of the crash.
