Another four people were injured, said a spokesman for the emergency services Osama Ali, who described the toll as still only "preliminary".
The explosions followed an offensive launched earlier this month by strongman Khalifa Haftar to take Tripoli.
At least seven powerful explosions rocked the city centre.
Shortly afterward, witnesses said, columns of smoke were seen above the district of Abu Salim in the south of the city, which was hit by a number of rockets.
It is the first time that the centre of Tripoli has been hit in the clashes which tend to calm down during night time.
No groups had yet claimed responsibility for the rocket strikes.
At least 174 people have been killed and 758 injured, including civilians, since Haftar's self-styled Libyan National Army (LNA) launched its offensive on April 4, according to figures from the World Health Organization.
In Geneva, WHO spokesman Tarik Jasarevic said that at least 14 civilians had been killed and 36 injured in the fighting.
The United Nations Office for the Coordination of Humanitarian Affairs (OCHA) calculates that more than 18,000 people have been displaced as a result of the clashes.
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