Russia suspended air traffic with the South Caucasus state in October of last year following Tbilisi's brief arrest of Russian army officers on spying charges.
Russian officials claimed the decision was based on the outstanding debt owed by Georgian airlines to Russia, whereas Georgia insisted the move was political.
"I think it is time to make certain steps [in improving bilateral relations], and the first such step must be restoring regular air links between the two countries," Gela Bezhuashvili said at a government meeting.
The minister praised Russia's recent decision to allow three charter flights from Tbilisi to Moscow during Easter festivities.
Russia has granted permission for Airzena Georgian Airlines to conduct three flights April 7, 10 and 11, but reaffirmed that the ban on regular flights remains in force and will be the subject of future bilateral talks.
Russia and Georgia agreed during bilateral consultations in February to set up a group to search for ways of settling Georgian airlines' debts, which Russia claims currently total $3.6 million.
Moscow has already restored postal links with Georgia, also suspended last year, and returned its ambassador and diplomatic staff to Tbilisi following what was the worst spat between the former Soviet allies since the Western-leaning Mikheil Saakashvili came to power in the ex-Soviet nation.