"Basically, the situation is back to the 2014 level, in our assessment," he said during a meeting of the Seimas' Committee on Foreign Affairs.
According to the minister, in recent days, there has been intense firing near the Eastern Ukrainian town of Avdiivka and clashes near Donetsk.
People in Avdiivka currently live "in the conditions of a humanitarian disaster" with power and heating supplies cut off, he said.
Linkevicius promised to Ukraine's ambassador in Lithuania, Volodymyr Yatsenkivskiy, who was also present at the meeting, that Lithuania would continue its political support for Ukraine.
"The international community's attention to Ukraine is decreasing and, therefore, more efforts on our part will be needed," the minister said.
The parliamentary committee also looked at human rights violations in Eastern Ukraine and the Russia-annexed Crimean Peninsula.
Yatsenkivskiy told the committee that 17 Ukrainians were currently in prison on Russia's territory due to political reasons.
"As the country aggressor, Russia continues to ignore the part of the Minsk agreements on the exchange of hostages and illegally detained persons," the ambassador said.
Russia annexed Crimea in 2014. In the same year, clashes between Moscow-backed separatists and Ukrainian government forces began in the eastern part of the country.