One of the hijackers told the flight crew he was "pro-Gaddafi" and he was willing to let all 111 passengers leave the Airbus A320, but not its seven crew, if his demands were met, the Times of Malta reported.
It was unclear what the demands were.
At about 1300GMT, women could be seen disembarking from the aircraft. Maltese Prime Minister Joseph Muscat tweeted the 25 people released were the first group of hostages freed.
About a half an hour later Muscat announced that 65 passengers had been let go.
Tim Diacono, a journalist from Malta Today, told Al Jazeera the hijackers had grenades and "threatened to blow the plane up".
"We don't know what the demands are, but the negotiations are under way," Diacono said. "There are people leaving the airplane as we speak, so it looks like it is being resolved peacefully, but it's still too early to tell."He said it was the first hijacking situation in Malta since the mid-1980s.
All passengers aboard the plane were in good health, an unnamed official at the Libyan foreign ministry told the state news agency LANA.
The prime minister's office confirmed a negotiating team was at Malta International Airport.