MOSCOW — Russia’s political order, largely unchanged since the early 1990s, was thrown into feverish uncertainty on Wednesday after President Vladimir Putin proposed sweeping constitutional changes that could extend his hold on power indefinitely.

Adding to widespread bewilderment, Putin’s loyal protégé promptly resigned as prime minister, along with the rest of the government.

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 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 by the prime minister, Dmitry Medvedev, that he was resigning. 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 Putin, 67.

Posing a question asked by many shocked observers, Dmitry Smirnov, a Kremlin reporter for the Komsomolskaya Pravda newspaper, said on Twitter: “Why has this all happened in a single day?” His answer: “It just means that those in Kremlin know history well: revolution has to be made swiftly, even if it’s a revolution from above.”

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In his speech Wednesday, Putin proposed amending the constitution to expand the powers of parliament, the prime minister and a body called the State Council. The council currently carries little weight — but should Putin step down as president and take it over, it could become the dominant power center, especially if the powers of the president are diminished.

Medvedev had hinted that his days might be numbered since the start of the year, when he delivered a melancholy New Year’s speech that quoted Russian writer Anton Chekhov: “We must not forget that the newer the year, the closer to death, the more extensive the bald spot, the more sinuous the wrinkles.”

At a meeting with his Cabinet and the president on Wednesday, Medvedev, a lawyer who has known Putin since they worked together in St. Petersburg in the 1990s and has helped him stay in power, linked his departure from the premiership to the proposed constitutional overhaul. It would, he said, “substantially change not only many articles of the constitution but also the balance of power — executive, legislative and judicial.”

The Russian Constitution limits a president to two consecutive terms, meaning that without a change, Putin would have to leave that office in 2024. But he has dropped hints about keeping his grip on power beyond that date.

With the clock running down on Putin’s final term, Russia’s political class has been abuzz for months with speculation about his intentions.

Some predicted a destabilizing succession crisis, but most expected the president to find a way to keep power despite constitutional term limits, as he did in 2008. That was when he left the Kremlin to become prime minister, with Medvedev serving as presidential place holder, until Putin returned as president in 2012.

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By leaving his reclaiming of the presidency to the last minute amid a tainted parliamentary election, Putin ignited a backlash of pro-democracy demonstrations. This time by starting the process four years early, he seems intent on avoiding abrupt and destabilizing changes.

Already in power as either president or prime minister for 20 years, longer than all modern Kremlin leaders since Stalin, Putin has now calmed an incipient and potentially disruptive succession struggle by leaving would-be successors and their backers in powerful agencies like the Federal Security Service guessing about what, exactly, they would be struggling over.

But this has set up a possibly wider fight among security and other bureaucratic clans over the reshaping of a system dominated by the executive that has been in place for more than 25 years.

The constitutional changes, which Putin said should be put to a popular vote, would be the first major overhaul of Russia’s political order since 1993, when the country’s first democratically elected president, Boris Yeltsin, subdued a rebellious legislature and then ordered a referendum to endorse a new constitution strengthening presidential power.

Unlike Yeltsin, who was deeply unpopular and faced an uphill struggle to get his new constitution approved by voters, Putin has amassed such overwhelming personal power and popular support that he can be confident of reshaping the system in virtually any way he wants.

His popularity, reinforced by the Kremlin’s tight grip on television and many other news media outlets, allows him to add a veneer of democratic legitimacy and avoid the path taken by China, where the Communist Party leader, Xi Jinping, has effectively established himself as leader-for-life through executive fiat.

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One scenario now considered likely is for Putin to leave his post as president and create a system similar to that of Kazakhstan. In that central Asian country, the longtime president, Nursultan A. Nazarbayev, stepped down last year as his country’s formal leader but stayed on as the head of the ruling party and took the new title of “leader of the people.”

This has established Nazarbayev as the equivalent of China’s former paramount leader, Deng Xiaoping, who had no formal executive position in his later years but remained in overall control of his country until his death in 1997.

It was not immediately clear whether the resignations of Medvedev and his Cabinet signaled a rift at the top of Russia’s hierarchy or — a far more likely possibility, according to most observers — were part of a well-coordinated but as-yet-unclear plan by Putin to hold onto power by reshaping the political system.

Medvedev’s replacement as prime minister is Mikhail Mishustin, an accomplished technocrat who is credited with modernizing Russia’s tax service. But as a virtual unknown bereft of close ties to the security apparatus, he is not regarded as a plausible successor to Putin.

Putin, by many accounts, had originally hoped to stay on top while stepping down as president by taking up a new supreme post as the leader of a united Russia and Belarus. But moves to unite the two countries, initiated by Yeltsin back in the 1990s, were resisted by Belarus and eventually stalled.

In a sign that Putin still ultimately depends on public support, he preceded his unexpected political moves by offering a grab-bag of handouts to the electorate in his State of the Nation speech. He promised free school meals, extra financial allowances for mothers who have more than one child and other measures focused on easing poverty.

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Real wages have mostly stagnated or fallen since Putin returned to the Kremlin in 2012 after the four-year interlude as prime minister. He has attributed the poor economic record to the Western sanctions imposed over his annexation of Crimea in 2014.

His political position, however, has remained unassailable, despite a flurry of street protests in Moscow and a few other cities last summer. The only real question has been whether and how he would engineer a way to again avoid term limits.

On Wednesday, Putin shed no light on his exact plans, but instead opened a Pandora’s box of possible options. The resulting uncertainty puts the political elite off balance, helping to ensure that Putin avoids becoming a lame duck and remains the pivot around which the country revolves.

Russian politics have become so centered on Putin and his hand-picked personal entourage that the prominent opposition leader, Alexei Navalny, in a mocking message on Twitter after Medvedev’s resignation, released what he said was “the shortlist of candidates for the new prime minister of Russia.”

He said it included “two of Putin’s bodyguards, Putin’s masseur, Putin’s gardener and Alina Kabaeva’s driver,” a reference to a former champion gymnast widely rumored to be Putin’s girlfriend.

The Kremlin quickly issued a statement announcing that Putin had in fact named Mishustin, the head of the Federal Tax Service.