The news came following Georgia's 4-0 home thumping at the hands of Group D rivals Poland in Friday's Euro 2016 qualifying clash.
That defeat left Georgia fifth in the group with three points from four matches, but with Scotland, Republic of Ireland and Germany all on seven and Poland top of the pool on 10, any hopes of reaching a maiden major tournament seem all but over.
Ketsbaia, formerly a player at AEK Athens and Newcastle United among others, tended his resignation in the aftermath of the defeat.
"I have already spoken at full length recently so I have nothing new to say," he said.
"Unfortunately my tenure with the national side has ended in a sad manner. From now on I will be supporting the team as an ordinary fan."
Alexia Putellas: "We’re already the only club to have won the men’s and women’s Champions League, so the only thing even more historic to do than that would be to win it in the same season"
‘Trent has won everything he can for Liverpool, but of those who’ve left that we wanted to stay, who’s actually done better? I can only come up with one’: Reds legend highlights potential danger of Alexander-Arnold moving to Real Madrid
