SOCHI, Krasnodar Region — President Dmitry Medvedev told United Russia on Thursday to prepare for challenges to its rule, suggesting that the Kremlin was ready to ease its grip on the regions to try to defuse social tension.

“United Russia is a leading political party now,” Medvedev told its leaders, who came to his Black Sea residence in Sochi to present their candidates for gubernatorial elections in the Sverdlovsk region in October. “This situation won’t last forever,” he said.

Political analysts said a relaxation of the Kremlin’s hold over the regions was a response to growing social tension and designed to create a safety valve for resentment toward Moscow.

Under the law as it stands, the president nominates the heads of 85 Russian regions for subsequent approval by local legislatures. The latest amendments mean that the local majority party rather than Kremlin envoys would present candidates for nomination.

“Other parties, if they succeed in the polls, will have similar rights [to propose candidates],” Medvedev told the officials, whose party now controls virtually all regional parliaments. “This will help develop political competition.”

Prime Minister Vladimir Putin is the leader of United Russia, but he does not hold any position in it.

During Putin’s presidency, elected governors became Kremlin-nominated officials. New election rules made it practically impossible for opposition parties to win seats in federal or parliamentary legislatures.

Medvedev has said the country needs a more flexible political system. He has ordered a lowering of the threshold of votes needed to earn a seat in the parliament and giving opposition parties greater opportunities to win seats.

He told United Russia leaders that changes to the rules for nominating governors were intended to make the process more transparent and give local political parties a bigger say.

“We have a special day today, new democratic times are beginning,” he said. “This is a step toward developing democracy in our country.”

Analysts said the proposals were intended to defuse social tension, fueled by the economic crisis, without sacrificing overall control of the provinces.

“In the days of economic boom, people eagerly voted for United Russia, which they associated with the Kremlin,” said Masha Lipman, an analyst at the Carnegie Moscow Center. “Now that they’re unhappy, they need a way to express their dissatisfaction,” she said.