However, the advisor believes that Hungary can still be persuaded by offering the country a transition period to phase out Russian oil imports.
"Hungary's blocking is disappointing," she told the Ziniu Radijas radio station. "The talks are ongoing and, as far as I know, the heads of the EU bodies have made considerable efforts to persuade the Hungarian government to agree to this package, including oil."
As the Hungarian government says that switching away from Russian oil would be "very expensive" and would require long-term structural reforms, "several ways out" are possible in this situation, according to Skaisgiryte.
"Probably the worst outcome would be if oil is taken out of this sanctions package," the advisor said.
"Another option would be to give Hungary a transitional period to implement this diversification and to allow it to gradually phase out Russian oil, something that is being considered for other countries that are heavily dependent [on Russian oil]," she said.
Without the oil embargo, the sanctions "would be much weaker than they could be" and the EU would continue to indirectly finance the war in Ukraine, "which is totally unacceptable to us", the advisor said.
"So it is necessary to do everything possible to get the Hungarians to agree to the sanctions on oil," she said.
The oil embargo would be part of the EU's sixth package of sanctions against Moscow over its invasion of Ukraine.