Russian authorities acknowledged a "significant" influx of cars trying to cross from Russia into Georgia on Saturday, days after Moscow announced partial mobilisation.

"There is a significant congestion of private vehicles... around 2,300" waiting to pass one checkpoint along the border, said the local interior ministry in a Russian region that borders Georgia.

The ministry urged people "to refrain from travelling" in the direction of Georgia.

It added that movement at the checkpoint was "difficult" and that additional traffic officers had been deployed.

The introduction of partial mobilisation in Russia on Wednesday sparked a new exodus out of the country.

The search "to leave Russia" was carried out 100 times more than normal on the morning of the announcement, Google Trends data showed.

Saturday's comments are the first official acknowledgement by Russian authorities of an influx of travellers out of the country.

Most direct flights to countries allowing Russian entry without visa have sold out, and prices have skyrocketed.

According to a law passed Saturday, servicemen who desert, surrender "without authorisation", refuse to fight or disobey orders can face up to 10 years imprisonment.

Russians fearing border closure and mobilisation also rushed to cross land borders. 

Borders with Kazakhstan and Mongolia also saw an influx of cars, with hours-long lines at crossings, witnesses said. 

The Kremlin on Thursday had dismissed reports that Russians eligible for mobilisation were rushing for exit as "fake".