"The main goal is to show that we are with Ukraine, with the people of Ukraine in their unequal struggle, and we regard the outpost here today as Europe's outpost to the East," Skvernelis, on his first visit eastern Ukraine, told reporters.
"It is very important to us how strong they are, how much they can protect their state and democracy," he added.
Avdiivka is close to the contact line between government troops and Russia-backed separatist forces.
Skvernelis said that it is shocking to see shelled-out apartment blocks and people living in appalling conditions in Europe.
The prime minister visited an outpatient clinic repaired using Lithuania's funds and a children's playground built with assistance of Lithuanian volunteers, and handed over digital terrestrial television transmitters to help Ukrainians broadcast their programs to areas controlled by Russia-supported separatists.
A representative of the civic organization Blue/Yellow also handed over humanitarian aid to local people and troops in Avdiivka.
The total value of the humanitarian aid amounts to around 100,000 euros.
On Thursday, Skvernelis is scheduled to meet with Ukrainian Prime Minister Volodymyr Groysman in Kiev and to open a security forum in the Ukrainian capital.