MOSCOW — President Vladimir V. Putin of Russia on Wednesday took the rare step of softening a government decision in the face of public pressure, diluting some parts of a much-despised pension overhaul that had prompted protests and dented his popularity.

Even as he announced the changes, Mr. Putin reiterated that demographic changes in Russia — particularly older adults living well past retirement age, while fewer young people are entering the work force — required some adjustments.

“I underscore once again that we have to make a difficult, complicated, but necessary decision,” Mr. Putin said, in a rare televised address broadcast nationwide at midday. “I ask you to be understanding about this.”

Mr. Putin warned that mushrooming costs now at $300 million per day could bankrupt Russia, and supporters lauded the speech, saying that he had stepped into his role of “father of the nation” to explain the hard facts facing the country.