Russian daily newspaper Kommersant reports that the possible spy may have been a man called Oleg Smolenkov.
Bakhtadze's resignation comes as the ruling Georgian Dream Party's popularity declines following the brutal dispersal of an anti-Kremlin protest.
The Kremlin does not agree with those who call what is happening a political crisis.
'People are starting to feel they’re in a dead end and that’s when their patience snaps and people go onto the streets.'
Russia has repeatedly denied allegations that it meddled in the 2016 US Presidential elections.
Critics of the channel, formerly known as Russia Today, accuse it of pro-Kremlin propaganda.
US investigators are probing alleged collusion between Russian agents and Trump's campaign.
Kremlin aide Yuri Ushakov hopes for the two leaders to meet properly.
Trump on Thursday scrapped the meeting over Moscow's seizure at the weekend of three Ukrainian ships and continued detention of a group of Ukrainian sailors.
Putin and Pence spoke in Singapore last week about key issues that could be discussed at the meeting between the two leaders, expected to take place at the G20 summit in Argentina in late November.
Moscow has repeatedly denied accusations it attempted to influence the vote that elevated Trump to the White House.
Trump's National Security Advisor John Bolton indicated during a trip to Moscow in October that the White House wanted a Paris meeting and Putin said he was interested.
The GRU has also recently faced accusations that it carried out large-scale cyber attacks including a foiled attempt to hack into the computer system of the global chemicals watchdog.
Putin spoke to the 82-year-old Saudi king by telephone on Thursday evening and they discussed the situation around the case of Khashoggi, the Kremlin said in a statement.
Researchers at the Royal United Services Institute (RUSI) in London said Russia often conducts cyber attacks to simply show it is capable of disrupting the networks of a potential enemy.
Investigative website Bellingcat this week published a picture of a decorated Russian military intelligence colonel it named as Anatoliy Chepiga who resembles one of the men spotted in the surveillance footage.
President Vladimir Putin's top critic was accused of violating a different protest law and faces up to 20 days in prison.
The Kremlin also suffered election blows in the far eastern region of Primorsky Krai and the southern Siberia region of Khakhasia, where its candidates failed to win in the first round.
A Russian Il-20 plane was hit by a Syrian S-200 air defence missile when it was landing following strikes by Israeli F-16 planes of western Syria on September 17.
Britain has said the two men were Russian military intelligence officers almost certainly acting on orders from high up in the Russian state.
Girlfriend and fellow Pussy Riot activist Veronika Nikulshina said in an interview that Pyotr Verzilov would be transferred to Berlin.
Russia resumed air strikes against insurgents in Idlib province on Tuesday after a hiatus of several weeks, according to a Syrian rebel and a war monitor.
Navalny, who was detained by police outside his home on Saturday, was found guilty of breaking the law by organising an unauthorised Moscow rally on Jan.
The Kremlin is confident that Trump genuinely wants to rekindle ties if he can get a political window of opportunity in Washington.
12Page 1 of 2