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Opposition lawmakers filed a case in a federal court alleging that routes were allocated "in an irregular manner" to the airline Avian, one of the deputies, Rodolfo Tailhade, said on the radio.
The lawmakers say low-cost carrier Avian is controlled by the Macri Group of the conservative president's family. They allege it and another company, FlyBondi, got preferential treatment in the allocation of the routes.
"They have been allocated the majority of the routes they asked for to the detriment of Argentine Airlines," the state company, Tailhade said.
Macri is already under investigation by prosecutors over alleged conflicts of interest in a government debt settlement agreed with the postal service previously controlled by his father's business.
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He has denied any wrongdoing.
Macri has been trying to steer Argentina out of recession since taking over as president in December 2015.
He faces a key political test in October this year when the country holds legislative elections.