"Ideally, it should be a European-level decision that would simply abolish the validity of these visas and everyone would stop issuing them," he told reporters before the Cabinet's meeting.
The minister's comment came after Tallinn decided to deny entry, as of Thursday, to Russian nationals who hold visas issued by Estonia.
However, Landsbergis said he doubted the effectiveness of such measures.
"A Russian citizen today can get a visa at the German consulate in any Russian city where there is a consulate, and travel via Finland, Estonia, Latvia, Lithuania or Poland to wherever they want to go for a holiday," he said.
This is why an EU-level decision is needed, according to the Lithuanian foreign minister.
Following the invasion of Ukraine by Kremlin forces, Lithuania was one of the first EU member countries to restrict the issuance of new Schengen and national visas to Russian citizens. Latvia and Estonia took similar decisions.
The Czech Republic, which now holds the rotating EU presidency, said last week that the bloc could add a blanket ban on visas for all Russian travelers to its sanctions against Moscow.