Ministers said they were now considering the possibility that the day-time blast on Monday outside Benghazi's Al-Jala hospital was not a deliberate car bombing as previously thought.
"All the signs point to an accidental explosion," Interior Minister Ashur Shwayel said at a press conference in Benghazi.
Justice Minister Salah al-Mirghani said it was "too early to draw any conclusions," but "among the theories being looked at, there is the possibility that this accident was not premeditated and that the explosion was not intended for this location".
The two people inside the car when it exploded have not yet been identified, the justice minister said.
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The health ministry, meanwhile, said in a statement that it has reached a "definitive toll" of three dead and 14 others wounded in the explosion.
On Monday, Libyan officials gave contradictory reports on the number of people killed.
Deputy Interior Minister Abdallah Massoud pointed to "15 dead and at least 30 wounded," while the health ministry said four people had died and six were wounded.
Immediately after the explosion, Libyan authorities denounced it as a "terrorist act", and an "odious crime".
Witnesses said children were among the casualties of Monday's blast, which also wrecked cars and scattered debris around the area.
Dozens of people, many of them youths, rushed to the scene, some volunteering to gather body parts and place them in plastic bags, AFP journalists reported.
On Tuesday, funerals and prayers were held for the victims attended by dozens of Benghazi residents angry at the lack of security in their city.
But previous attacks, bombings or assassinations, have rocked the city by night or in the early hours when the streets are empty, and have hit non-civilian targets, especially security officials.
Four police stations have been bombed in Benghazi since last Friday, causing damage but no casualties.
Authorities blame radical Islamists for the violence, including a deadly attack in September against the US consulate in Benghazi that killed ambassador Chris Stevens and three other Americans.