Sources familiar with the discussions told NBC News that Russian President Zelenksyy asked the Biden administration to designate Russia as a state sponsor of terrorism.
The sources said Zelenskyy made the request in a recent phone conversation with President Joe Biden.
The request didn't carry the same priority as urgent appeals for more weapons and energy sanctions against Russia, the sources said.
The Washington Post first reported on the request.
Asked if the U.S. would designate Russia as a state sponsor of terrorism, White House press secretary Jen Psaki and Secretary of State Antony Blinken both left open the possibility.
Blinken said on March 17 that they are looking at everything and we will look at everything.
There are only four countries currently on the U.S. list of state sponsors of terrorism: Iran, North Korea, Syria and Cuba.
The designation triggers some of the most aggressive sanctions the U.S. government could take on a country, with restrictions on financial transactions and defense exports and sales, as well as foreign aid.
The Biden administration has imposed severe financial and other sanctions on Russia, including blocking access to half of its foreign reserves. It is not clear how such a designation would affect Russia's economy.
According to some legal experts, if Biden blacklists Russia as a sponsor of terrorism, any company, individual, or state that wins a court judgment against Russia could demand access to any blocked or frozen assets of the Russian government or Russian oligarchs.
The designation could allow Russian officials to file lawsuits in U.S. courts against Russian officials, as well as lift diplomatic immunity on them.