Russia’s political order, largely unchanged since the early 1990s, was thrown into feverish uncertainty on Wednesday after President Vladimir V. Putin proposed sweeping constitutional changes that could extend his hold on power indefinitely. Adding to widespread bewilderment, Mr. Putin’s loyal protégé promptly resigned as prime minister, along with the rest of the government.

Mr. Putin described his proposals, announced in his annual state of the nation address, as an effort to enhance democracy. But his political rivals and many independent analysts interpreted them more as a strategy for keeping power after the end of what is supposed to be his final term in 2024. Mikhail M. Kasyanov, a former prime minister under Mr. Putin who is now a fierce critic, said the president had given a “clear answer” to questions about his future: “I will remain president forever.”

Few others found that degree of clarity, especially after the surprise announcement shortly after Mr. Putin spoke that Prime Minister Dmitri A. Medvedev was resigning. Mr. Medvedev then took a new job as deputy head of the Security Council, an important body but one that will leave him little space, since it is headed by Mr. Putin.