The exchanges with heavy weapons, that rival armed groups retain from the 2011 NATO-backed uprising which toppled longtime dictator Moamer Kadhafi, were heard in the city centre, 25 kilometres away, AFP correspondents reported.
An airport official said "rockets struck inside the airport interrupting flights.
"Clashes followed between the Zintan militia who control the airport and rivals who want to drive them out," the official added.
The former rebel militia from Zintan, a hill town southwest of the capital, are the main supporters of liberals in parliament who are trying to resist attempts by powerful Islamists bidding for power in the vacuum left by Kadhafi's ouster.
"The revolutionary forces arrive within the perimeter of Tripoli airport and clash with armed groups inside," it said on its Facebook page.
The fighting comes weeks after a contested general election to replace the Islamist-dominated General National Congress which has been mired in controversy and accused of hogging power.
Libya, awash with weapons since the end of the 2011 uprising, has also been plagued by growing lawlessness while on the political front rivals cabinets are jostling for power.
"The United States is deeply concerned by the ongoing violence in Libya and dangerous posturing that could lead to widespread conflict there," State Department spokeswoman Jen Psaki said.
"We affirm our support for Libya's democratic transition and urge the seating of the new Council of Representatives as soon as possible," she added.
She insisted that drafting a new constitution "must advance without interference or violence".
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