The EU's fifth package of sanctions against the Minsk regime over its "continued human rights abuses and the instrumentalization of migrants" came into force on Thursday.
"This EU sanctions package shows that the EU stands united and will not tolerate the cynical and brutal actions of the Lukashenko regime, either against the people of Belarus or against vulnerable migrants from far away countries," the Lithuanian Foreign Ministry quoted Landsbergis as saying in a press release.
"If the Minsk regime continues its illegal actions, the EU has the instruments to consider new sanctions packages," he added.
The latest package imposes restrictive measures on an additional 17 individuals and 11 entities that have contributed to organizing illegal migration for political pressure purposes and to the repression of people in Belarus.
The sanctions target, among others, prosecutors and judges of the Belarusian regime, as well as Belavia Airlines, Hotel Planet and the tourist agency Tsentrkurort.
The new package took effect after it was published in the Official Journal of the EU on Thursday.
Brussels accuses the Minsk regime of carrying out a "hybrid attack" against the EU by luring thousands of migrants from the Middle East and diverting them to the borders of Poland, Latvia and Lithuania.
Lukashenko denies he is responsible for the migrant influx.