"Today's [deal] put an end [to discussions]. Even though we had walked on a very narrow path, we found the compromise that was necessary. I think today we can be happy with the result," Nauseda told journalists after the European Council's meeting in Brussels.
EU leaders agreed to impose an embargo on Russian oil transported by sea. The ban, which will not affect pipeline oil imports, is a compromise to win the backing of Hungary and other countries reliant on Russian resources.
European Commission President Ursula von der Leyen said the ban "will effectively cut around 90 percent of oil imports from Russia to the EU by the end of the year".
Nauseda said, "This is an extremely important decision, let's not be afraid of that word."
"The sixth package of sanctions had stalled for almost a month, which was great news for the Russian regime," he noted.
The sixth package also involves disconnecting Sberbank, Russia's biggest commercial bank, from the global SWIFT system, among other restrictions.
According to the Lithuanian president, the sanctions will have an impact on the Russian economy.
He said earlier on Monday that once the EU agreed on the sixth package, it would be necessary to "consistently increase pressure" on Russia and move on to the seventh round of sanctions, adding that Lithuania would seek that it include an embargo on Russian natural gas.
However, Nauseda said early on Tuesday that some countries had warned in advance that they would not back such a ban.
"I wouldn't want us to start talking about the seventh package of sanctions by saying that we will not consider this or that," he said. "I see a certain tendency to want to make sure that the seventh package does not include gas or some other energy resource."
EU leaders on Monday evening also discussed how to help Ukraine to ship its grain out of the country amid Russia's blockade of its seaports, according to Nauseda.