The government decree, signed on November 28, orders the Russian Defense Ministry to hold negotiations with Egyptian officials and to sign the document once both sides reach an agreement.
Russian Defense Minister Sergei Shoigu visited Cairo for talks with Egypts political and military leadership on Wednesday and the decree said the draft had been preliminary worked through with the Egyptian side and approved by Medvedev.
Russia launched a military operation to support Syrian President Bashar Assad in September 2015 and there are signs it is keen to further expand its military presence in the region.
U.S. officials said in March that Russia had deployed special forces in Egypt near the border with Libya, an allegation Moscow denied.
Russia has cultivated close ties with powerful Libyan commander Khalifa Haftar, who held talks with Shoigu, the Russian defense minister, via video link from a Russian aircraft carrier in the Mediterranean this year and visited Moscow.
Russian and Egyptian war planes would be able to use each others air space and airfields by giving five days advance notice, according to the draft agreement, which is expected to be valid for five years and could be extended.
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