According to the Washington Post, Ukrainian President Volodymyr Zelensky made the appeal in a phone call with US President Joe Biden this week.
Biden did not commit to specific actions during that call, the newspaper reported, citing people familiar with their conversation.
It said the label can be applied to any country that has "repeatedly provided support for acts of international terrorism."
According to the Reuters news agency, the list currently includes four countries, North Korea, Cuba, Iran and Syria.
Biden has described Russia's actions in Ukraine as amounting to genocide.
Polish President Andrzej Duda said on a visit to Kyiv this week with his Lithuanian, Latvian and Estonian counterparts that “those responsible for crimes against the Ukrainian people must be punished by international tribunals.”
He also appealed for “sanctions that will exclude Russia” from the international community.
In a major speech in Warsaw last month, Biden told the world that Vladimir Putin should no longer remain in power amid Russia's brutal war against Ukraine.
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Source: IAR, PAP, Washington Post, Reuters, cnbc.com