WASHINGTON — Secretary of State John Kerry warned his Russian counterpart on Saturday that steps by the Kremlin to annex Crimea would “close any available space for diplomacy,” a State Department official said.

Mr. Kerry’s warning came after leaders of Russia’s Parliament said they would support a move by Crimea to break away from Ukraine and become part of the Russian Federation.

He said during his recent trip to Europe that he had provided “suggestions” to Sergey V. Lavrov, the Russian foreign minister, on how the crisis set off by Russia’s military intervention in Crimea might be resolved.

“We have made suggestions to Foreign Minister Lavrov, which he is currently taking personally to President Putin in Sochi,” the secretary of state said Thursday, after meeting with Mr. Lavrov in Rome.