Rostransnadzor, the country's transportation watchdog, "issued an order to Kogalymavia" giving it until Monday to carry out the checks, said Anastasiya Dombrovskaya, an official for the agency.
Contacted by AFP, Kogalymavia said they received the instructions but denied that this amounted to a de-facto grounding of the company's remaining fleet of six A321 airliners.
The company, which runs charter flights for tourist operators, also has two A320 planes, according to its website.
The Russian air transport agency meanwhile said it had started a snap month-long inspection of Kogalymavia.
Russian investigators have launched two probes into the crash and a team of criminal experts are working at the crash site, together with air transport officials and rescue workers.
The spokesman of Russia's Investigative Committee, an equivalent of the FBI, Vladimir Markin, said Sunday that investigators had questioned Kogalymavia service workers who had examined the aircraft in the Russian airport of Samara on the Volga river before it flew for Egypt on Friday.
Some bodies from the wreckage in a remote part of the restive Sinai Peninsula were to be flown to Russia from Cairo morgues on Sunday evening, emergency ministry officials said.
