Machine gun fire reverberated through the largest city Almaty after days of unrest sparked by a fuel price hike.
Officials have reported deaths of police and protesters.
The president has blamed foreign-trained "terrorists", without giving evidence.
In an address on state TV on Wednesday, President Kassym-Jomart Tokayev appealed to the Russian-led Collective Security Treaty Organisation (CSTO) for support in quelling the protests. The bloc includes Russia, Kazakhstan, Belarus, Tajikistan and Armenia.
The overseas force being sent to Kazakhstan reportedly numbers about 2,500 soldiers. The CSTO says the troops are a peacekeeping force and will protect state and military installations. They will stay in the country for several days or weeks, the Russian RIA news agency reports.
The US State Department has said it is closely monitoring the deployment of Russian troops. "The United States and, frankly, the world will be watching for any violation of human rights," a spokesman said.
"We will also be watching for any actions that may lay the predicate for the seizure of Kazakh institutions."
The UN, US, UK, and France have called on all sides to refrain from violence.
Some 18 members of the security forces have died in Almaty, officials said, and police said they had killed dozens of people described as "rioters" overnight.
Saule, a 58-year-old construction worker who took part in the protests, told AFP news agency that she saw security forces open fire on demonstrators.
"We saw the deaths," she said. "Straight away about 10 were killed."
Kazakhstan's interior ministry says 2,298 protesters have also been detained.
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