Are there nonstop flights from Rome (FCO) to Tbilisi (TBS)?

Yes. Georgian Airways fly this route. Flight time is about 3h 40m.

What is the fastest connection from Rome (FCO) to Tbilisi (TBS)?

via Istanbul ≈ 4h 12m, via Istanbul ≈ 4h 13m, via Thessaloniki ≈ 4h 14m (estimated flying time, excluding layovers).

from 15,000 ANA miles, from 23,000 JAL miles (economy, one way, based on the published award charts).

Rome–Fiumicino Leonardo da Vinci International Airport (FCO) to Tbilisi International Airport (TBS)・2,697 km

Nonstop flights available (1 airline). Flight time about 3h 40m. Nonstop return flights also operate.

With milesANA 15,000 miles+ (via IST)JAL 23,000 miles+ (via CDG)Economy, one way, estimate. Tap a connection for miles by cabin.

37 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.