"I told the prime minister today, in fact last night, that I was ready to step down, and I am waiting for the prime minister's decision," Landsbergis, chairman of the ruling conservative Homeland Union–Lithuanian Christian Democrats, told reporters.
"I understand the reputational damage to Lithuania," he said.
The US sanctions on Belaruskali, which exports its products via the Lithuanian port of Klaipeda, were announced in August and came into force on December 8.
Lietuvos Gelezinkeliai (Lithuanian Railways, LTG) says shipments continue as an advance payment made by Belaruskali in November is sufficient to cover the cost of rail services in December and, possibly, part of January.
The state railway company said it had informed the Transport Ministry and the Foreign Ministry about the advance payment.
Landsbergis said, however, that LTG had only informed his ministry about Belaruskali's advance payment in September for services in October.
It was not informed about "the subsequent payments that took place", he said.
LTG Cargo, the group's freight transportation subsidiary, previously handled over 10 million tons of Belaruskali shipments, worth around 60 million euros, on average annually.
A week ago, the US expanded its sanctions to include Belarus Potash Company (BPC), Belaruskali's exporting arm, with US companies given until April 1 wind down business dealings with the company.