BISHKEK, Kyrgyzstan — A Russian-led military alliance will begin withdrawing its troops from Kazakhstan in two days, the country’s president announced on Tuesday, saying they had fulfilled their primary goal of helping stabilize the Central Asian nation as it experienced the worst political crisis in its history.

In a speech to senior government officials and members of Parliament, President Kassym-Jomart Tokayev said the withdrawal would take “no more than 10 days.”

In Moscow, Russia’s defense minister, Sergei K. Shoigu, did not mention specific plans for the troops to withdraw. Speaking at a meeting with the military top brass, he said that the Russian-led soldiers would “continue their mission until the situation fully stabilizes” but that it would be “up to the Kazakh leadership” to decide when that happens.

Regardless of when the 2,500 Russian-led troops do leave, the operation is already regarded as a geopolitical triumph for President Vladimir V. Putin of Russia, who can present himself once again as an effective crisis manager for countries that Moscow considers within its sphere of influence. For Mr. Tokayev, the rapid dispatching of troops buttressed his grip on power at a time when it was most shaky.

In his speech, Mr. Tokayev also announced several economic measures, including a five-year salary freeze for top public officials, and promised to destroy corrupt schemes that are widely believed to have benefited the country’s oligarchs.

Kazakhstan is part of an economic union with Russia, but because of its oil wealth it had been proud of retaining more autonomy than many other former Soviet states. A swift exit of the soldiers would most likely bolster Mr. Tokayev’s image, even if it exposed the vulnerability of post-Soviet strongmen leaders, who have been forced to turn to Moscow when their rule is threatened.

Daniil Kislov, an expert in Central Asia and editor of Fergana, a website that covers the region, said that by inviting the troops in “Tokayev gave a real gift to Putin.”

“Putin is happy to use any opportunity to expand somewhere, be it Ukraine or some other unstable country where a good helping hand of Moscow might be needed,” he said.

The crisis in Kazakhstan erupted last week after peaceful protests in the country’s west over a spike in fuel prices suddenly spread to the rest of the country. The unrest turned Almaty, the country’s biggest and most populous city, into a war zone with government buildings ablaze.

More than 2,000 people have been injured so far, according to the government, and the health ministry issued, then withdrew, a statement on Sunday saying that at least 164 people had died in the violence. Nearly 10,000 people have been detained, according to the government.

Mr. Tokayev said he made the decision to seek help from the Collective Security Treaty Organization, the Kremlin-led version of NATO for a group of former Soviet countries, at the time when the Kazakh government “could lose control over Almaty completely.”

Mr. Tokayev spent most of his career serving the state created by Nursultan Nazarbayev, the long-ruling former president who stepped down in 2019 and picked him as his successor. But in his speech, Mr. Tokayev seemed to lay the blame for his country’s upheaval squarely on his mentor’s shoulders.

Without mentioning Mr. Nazarbayev by name, he denounced the country’s endemic cronyism and income inequality, and said that thanks “to the first president” a group of people “wealthy even by international standards” has emerged.

“I think it is time they pay their dues to the people of Kazakhstan and help them on a systemic and regular basis,” he said.

There is little serious political opposition in Kazakhstan, where protesters and activists face constant harassment or are pushed to leave the country. But Mr. Tokayev’s rare rebuke of his predecessor was indicative of the political infighting taking place at the highest echelons of power.

Over the past week, Mr. Tokayev has reshuffled Kazakhstan’s security bloc. Karim Masimov, the head of the main security agency who was widely seen as Mr. Nazarbayev’s close ally, was fired at the height of the crisis and later arrested on suspicion of treason. Several other high-ranking officials have been dismissed, local news media reported, citing government agencies.

Only 162 people control half of Kazakhstan’s wealth, according to a recent report by the accounting firm KPMG.

“Kazakhstan has the facade of a so-called modern country,” said Elmira Satybaldieva, whose research at the University of Kent focuses on inequality and labor rights in Central Asia, “but if you scratch the surface, there is horrendous economic disparity and discontent that has been brewing for decades.”

Kazakhstan, the most prosperous of the Central Asian nations, is believed to have one-twelfth of the world’s proven oil reserves, according to the U.S. Energy Information Administration. It also produces about 40 percent of the world’s uranium.

Yet rampant inequality means that only 3.5 percent of the adult population has an annual income above $10,000. The country’s minimum monthly wage is about $100. Eighty percent of the economic population is in “deep debt,” and cannot afford proper housing, Ms. Satybaldieva said.

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