"I'd suggest considering additional sectoral sanctions if people are barred from leaving. The European Union has the instruments," he told reporters. " Speaking in the language he [Alexander Lukashenko] understands is right way to go."
According to Lithuania's top diplomat, the Iraqi government is currently arranging a flight for compatriots stranded at the border.
"About 200 people have signed up for it," he said. "With more flights and a safe passage to the airport, I think a lot of people could be saved."
Landsbergis expects the EU's recently agreed sanctions against the Minsk regime for triggering the migrant crisis to take effect shortly.
"The list should be finalized in the next few days. It consists of almost 30 items, individuals and legal entities," he said.
The minister was skeptical about outgoing German Chancellor Angela Merkel's phone call to Lukashenko on Monday, saying that such conversations are risky as they can be used "to legitimize oneself".
"The dictator will do everything he can to make this conversation look like negotiations and to create as much confusion as he can," Landsbergis said. "It is his aim to weaken us, to weaken our position, to make us doubt each other."
Lithuania's top diplomat noted that one's position can be conveyed to Minsk via the EU's representative.
"There can be no negotiation under any circumstances," he said. "I believe that when EU Foreign Minister Josep Borrell speaks, it is the right way to go."
"He spoke to Mr. [Belarusian Foreign Minister Vladimir] Makey yesterday. We know exactly what he said; we know the content of his conversation; he has the authority," Landsbergis said.
"[Borrell] demanded that people be allowed to leave the border immediately, that a safe corridor be created for them to leave Belarus through the airports and to return home," the Lithuanian foreign minister said.
"I support such a position if there is a consensus among the 27 member states," he added.
Several thousand migrants camping on the Belarusian side of the frontier for more than a week keep attempting to force their way into Poland.
Fearing a similar scenario, Lithuania last Wednesday declared a state of emergency along its border with Belarus and at irregular migrant accommodation facilities.
Over 4,200 irregular migrants have crossed into Lithuania from Belarus illegally so far this year.
Lithuania and other Western countries accuse the Minsk regime of orchestrating the unprecedented migration influx, calling it "hybrid aggression".