"This is not assistance; this is blackmail," Landsbergis told BNS via his spokeswoman, Vytaute Smaizyte, on Monday evening. "We do not expect anything different from the terrorist regime."
"The answer is simple: if Minsk does not stop and continues to bring in migrants, Lithuania will propose new sanctions".
Belarus' authoritarian leader said earlier on Monday that his country was ready to help Lithuania deal with the migrant crisis, but it would do so "not for free ".
"If they need help, we will provide this help, but no longer for free," Belarus' state news agency BelTA quoted Lukashenko as saying in an interview with Sky News Arabia.
Lukashenko added that efforts to counter cross-border criminal activity, such as illegal migration and arms or drug smuggling, required considerable resources.
"If you want us to help you with that, don't try to choke us," BelTA quoted the authoritarian leader as saying.
"They've introduced sanctions against us. They've decided to choke my country, my people. I am the president of this people. I have to evaluate the situation and take certain actions to prevent the choking of the people and the destruction of the country. They take such steps against the Belarusian people and yet they want us to protect them in this situation? Listen, it is at least strange," he said.
So far this year, Lithuanian border guards have detained over 2,000 illegal migrants crossing its frontier – an external EU border – from Belarus, compared to just over 80 in the whole of 2020.
Vilnius says the migration influx is an organized campaign by the Belarusian regime against Lithuania.
Tensions between Minsk and Vilnius soared in the wake of last year's controversial presidential election in Belarus.
The Lithuanian government has declared a state of emergency due to the growing migrant crisis.