"Sceptics may disagree, but I see unity at European level as well," Nauseda posted on Facebook.
"Yes, there are different opinions. There is a lot of unnecessary discussion and squabbling, and delays, but, nevertheless, at a crucial moment, Europe demonstrates its ability to agree," he added.
According to the president, this shows that Russia's strenuous efforts to sow divisions among EU member countries are failing.
"The aggressor will not get good news. The sixth package of sanctions, just adopted, is certainly not the end," Nauseda wrote. "Measures targeting Russia's economy, finance, trade, transport, propaganda channels, war criminals, oligarchs and others will continue."
"Today, Russia has not yet felt the full impact of the sanctions, but it will. Soon enough," he added.
As Ukraine marks 100 days since Russia's invasion on Friday, Nauseda said that the Ukrainian people "are fighting with perseverance and heroism against the far larger forces of the aggressor. Against murderers, rapists, looters and marauders whose bloodthirsty crimes horrify the whole world".
The president said that Lithuania "gives its heart to Ukraine" and urged Lithuanians to remain united and to help the heroes.
Ukraine has been fighting Russia's invasion for more than three months and is calling on Western countries to send it more weapons.
Russian forces have been recently trying to consolidate their hold on the occupied territories in the eastern Donbass region.