Burns, speaking at a foreign policy event at Georgetown University in Washington, D.C., also said Xi maintains serious ambitions over Taiwan and warned that conflict over the island nation would be "deeply unfortunate" for all involved.
China, which signed a "no limits" partnership with Russia last year, has refrained from condemning its invasion of Ukraine even as Western countries, led by the United States, imposed sweeping sanctions against Moscow.
But Burns, who traveled to Ukraine recently to meet with the country's president, said Xi was likely surprised and unsettled by what he described as the poor performance of Russia's military.
Burns added that Russia and China's friendship is not totally without limits.
Speaking on Moscow's invasion, Burns said the next six months will be "critical" for Ukraine, where Moscow has been making incremental gains in recent weeks.
Burns also spoke on issues in the Middle East. He said Iran's government was increasingly unsettled by affairs within the country, citing the courage of what he described as "fed up" Iranian women.
Burns also said he was concerned about prospects for greater violence between Israelis and Palestinians.
(Reporting by Michael Martina; Writing by Rami Ayyub; Editing by Christopher Cushing)
By Michael Martina
