Orly airport said it was lodging a public order complaint after the ruckus between Booba and Kaaris forced airport officials to temporarily shut down a departures hall packed with people heading off at the height of the holiday season.
French prosecutors said Thursday custody would be extended for the two rappers and ten members of their entourages.
"The video investigation is continuing," they told AFP.
Fourteen people were initially placed in police custody on Wednesday afternoon, with two released on Thursday morning, a judicial source said.
Aeroports de Paris (ADP), which manages the capital's airports, said the fight had damaged Orly's image and "endangered the lives of others."
ADP added the disturbance had meant it was not possible to place a security cordon around an abandoned item of luggage. Air France has also made a complaint.
Some passengers who suffered brief delays to their flights filmed the brawl, which led to the damage of a duty-free store, and posted the footage to social media.
The two rappers had been due to perform Wednesday evening in Barcelona.
According to Kaaris' lawyers Arash Derambarsh and Yacine Yakouti, the rapper, who was accompanied by six people, was surrounded by "a dozen people who have nothing to do with music and were just looking for a fight. "He was taken aside by Booba, who insulted his child and his wife.
Then they all jumped on him. You see it on the videos, they were three against one," said Derambarsh, who said his client reacted in self-defence.
He added the assailants used perfume and glass bottles as weapons.
Booba's lawyer Yann Le Bras responded by telling BFM TV the video footage showed it was Kaaris and his group whose behaviour had been "very aggressive".
Booba, 41, and Kaaris, 38, have known each other since 2011, by which time Booba had already carved out a name for himself.
The pair have since waged a feud over social media where some posters indulge in anything from simple mockery to calls to settle differences through fighting.
Booba, one of France's most popular rappers, has reportedly fallen out with Kaaris in the past after failing to support him in a dispute with fellow French artist Rohff.
Rohff was sentenced in November to five years in jail for aggravated assault in a clothes boutique owned by yet another rapper, Unkut.
Booba has also been involved in other fights in recent years - notably with La Fouine with whom he clashed in Miami in 2013.
Some rapper spats have turned fatal in the United States where hip-hop singer Christopher "The Notorious BIG" Wallace was gunned down in 1997, a year after Tupac Shakur suffered a similar fate.
Booba, whose often raw and violent tracks evoke life on the street in the Paris suburbs, symbolically 'killed' Kaaris, La Fouine and Rohff, depicting their decapitation in an animated clip for his track "Gotham," in which he appears as Batman.
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