"At the moment, I really see no reason for him to step down. If this problem continues, however, then there will be no other solutions," he told LRT Radio on Tuesday morning.
Several landowners in the district of Klaipėda have accused the minister's family of farming their land without their permission.
The 15min.lt news website reported last week that Markauskas' mother, Sofija Markauskienė, had been using several plots of land in the western Lithuanian district without the landowners' permission for five to six years and that she had been receiving payments from the National Paying Agency for that land.
President Dalia Grybauskaitė said on Monday that "the shadows of abuse" falling on the minister and his family "damage not only his reputation, but also the reputation of the government as a whole".
Markauskas on Monday described the situation as an unintentional mistake.
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