After a week that brought a rare show of mass dissent in Russia, Prime Minister Vladimir V. Putin on Friday warned the members of United Russia, the party he leads, that they must win back the loyalty of the people. “You can’t, of course, promise everything to everyone right away,” he said. “You cannot turn into ‘Mr. Promises,’ who makes promises just to pull the wool over people’s eyes, to break into positions of power, and then goes about solving his own personal problems without thinking about fulfilling your promises.” Mr. Putin’s remarks came a week after an antigovernment rally in Kaliningrad drew 6,000 to 10,000 people, the largest turnout Russia has seen in years. He told party members that it was “completely obvious, and right, that citizens turn to us with complaints about various aspects of our activities,” and instructed them to pay close attention to those complaints.