Landsbergis said in a press release after an informal meeting of the bloc's top diplomats in Prague that "we succeeded in convincing all EU countries that millions of Russian citizens with Schengen visas are a problem not only for the countries bordering Russia, but also for the EU's regional security".
"Together with Estonia, Latvia and Poland, we will work in the coming weeks to find solutions that will help to significantly limit the flow of Russian tourists," he said.
EU foreign ministers agreed earlier on Wednesday to suspend a 2007 visa facilitation agreement with Russia.
The measure does not mean a formal ban on tourist visas as requested by some of Russia's EU neighbors, including Lithuania.
EU foreign policy chief Josep Borrell said the suspension of the deal will make it "more difficult" and "longer" for Russian nationals to obtain visas.