This file photo taken on July 28, 2022 shows Russian tourists having their passport checked at the Nuijamaa border crossing, Finland.AFP
Gabrielius Landsbergis said he expected talks with Latvia, Estonia, Finland and Poland on the issue in Prague next week on the sidelines of an EU foreign ministers' meeting.
"We seek a European solution in the first place, because it is the most sustainable and legally correct," Landsbergis told reporters in the Lithuanian capital Vilnius.
"If we don't reach one, we do not rule out the possibility of looking for a regional solution that would include the Baltic states, Poland and potentially Finland," he added.
The minister said there should be no Russian tourists in the EU "as if nothing happened".
Eastern EU countries stopped issuing new tourist visas to Russians shortly after Moscow began its invasion of Ukraine on February 24.
But Russians with visas issued by other EU countries are allowed into all EU states because of the bloc's rules on free movement.
The European Commission acknowledged last week that discussions were underway to see if a "coordinated approach" on Russian visas could be reached.
But German Chancellor Olaf Scholz has expressed reservations about such restrictions.
Landsbergis said even a regional decision will be "difficult" to reach.
"We want the rules, if agreed, to be applied equally. In other words, a person who was denied entry in Estonia would not receive a different response in Latvia or Lithuania," he said.