"Based on information available to us, up to 6,000 (are stranded abroad). But these are figures that came in after our call for registration and they should be updated," the minister told LRT Radio.
"We believe that up to a thousand should have returned by now," he added.
Most of the citizens are stranded in Spain, the United Kingdom and France. Also, about 1,500 people are stuck in countries outside of the EU, making it more difficult for them to get home.
Linkevicius urged citizens to register for repatriation flights, warning that there might be no alternatives to return to Lithuania in the future.
According to the minister, the situation on the German-Polish border, where many Lithuanian nationals were left stranded after Poland refused to allow passenger cars through, is easing.
Eight convoys of buses and minibuses have been allowed to transit through Poland to reach Lithuania. Passenger cars are being directed to the ports of Sassnitz and Kiel for ferries to Lithuania or Latvia, and Lufthansa will continue to operate flights from Frankfurt to Vilnius until Sunday.
Lithuanian citizens could also take LOT flights to Warsaw Airport, which is open to transit by all EU nationals, from some countries. Commercial flights would then have to be arranged to fly them to Lithuania, Linkevicius said.