MOSCOW — President Vladimir V. Putin on Saturday eased a sweeping ban on public protests in Sochi, Russia, starting on Tuesday and continuing through the Olympic Games next month and the Paralympic Games in March. However, any demonstrations will require approval in advance from the authorities.

The ban, which Mr. Putin ordered in August, had prompted criticism from rights groups and concern from the International Olympic Committee. The new order, posted on the Kremlin’s website, seemed to be an effort to burnish Russia’s reputation before the Olympics. It followed the release of some of the nation’s most prominent prisoners, including the tycoon Mikhail B. Khodorkovsky, two performers from the punk band Pussy Riot and 30 Greenpeace activists.

The announcement completed plans that had been in the works to allow approved protests at a park in the Khosta district, about halfway between central Sochi and the Adler district, where the main Olympic Village is.

“Please, everybody, welcome,” Dmitry Chernyshenko, president of the Olympic organizing committee, said in December when asked about criticism of Russia on issues like political freedoms, gay rights, and environmental damage from construction in Sochi. “You’re free to express those opinions during the Games.”