The meeting was aimed at discussing relations between the two countries amid escalating tensions between Moscow and Washington, Reuters news agency reported.
The Press Office of Russian Security Council issued a statement, confirming the talks between the two officials on relations between the two countries but did not elaborate on the details.
A US Embassy spokesperson said Burns was leading a delegation of senior US officials to Moscow on Tuesday and Wednesday at President Joe Biden's request.
"They are meeting with members of the Russian government to discuss a range of issues in the bilateral relationship," the spokesperson said.
Neither side gave details of the conversation, but security issues loom large in their troubled relationship.
MA/PR