Approximately 1,000 more people have crossed the Russian-Estonian border to return to the EU in recent days after countries closed their airspace to Russia.
ERR's Narva correspondent said the situation on the border is calm but many people are returning with large suitcases.
Aleksandr Kazmin, field manager of the Police and Border Guard Board (PPA), said Estonia is being used as a transit country: "Planes were canceled and people who were in Russia are taking the opportunity to go to other countries through the Narva border crossing."
Many EU citizens are leaving Russia quickly because they say attitudes towards them have changed.
Francisco, a Spaniard, worked for a car company in Moscow for 16 years but has decided to leave.
"They called me a traitor. I'm not a traitor, I love Russia, but I can't justify such a war, it's criminal. The risk is high, Spanish citizens shouldn't be in Russia right now," he said.
"I'm trying to help a friend cross the border who can't get through because he has a daughter without a passport."
ERR's correspondent said some residents of Narva have been visiting the Russian border city of Ivangorod as the exchange rate continues to fall.
Editor: Helen Wright