Several residents crossing the Bugristoe border checkpoint into Russia have cited concerns over violent protests in Kazakhstan's largest city Almaty.
Dozens of Kazakh residents have been fleeing into Russia, as widespread violent unrest plunged the country into chaos.
Those crossing Kazakhstan's Bugristoe border checkpoint on Saturday said they had family in Russia and cited concerns over the protests and a lack of internet.
"Everything is destroyed, absolutely all buildings, it is as if it were a real war, you know, absolutely all shopping centres, absolutely all restaurants, cafes, everything is destroyed," said one resident.
Meanwhile, Russia has continued to send troops to Kazakhstan at Kazakh President Kazzym-Jomart Tokayev's request.
The Collective Security Treaty Organization, a Russia-led military alliance of six former Soviet states, authorised sending about 2,500 mostly Russian troops to Kazakhstan as peacekeepers.
US Secretary of State Antony Blinken on Friday challenged Russia's justification for sending forces into Kazakhstan after days of violent unrest in the Central Asian country.
"One lesson of recent history is that once Russians are in your house, it's sometimes very difficult to get them to leave," Blinken said.
Russia's foreign ministry called Blinken's remark "typically offensive" and accused him of joking about tragic events in Kazakhstan.
It said Washington should analyse its own track record of interventions in countries such as Vietnam and Iraq.
More than 4,000 detained
On Saturday, there were no immediate reports of unrest in Almaty, but police dispersed a demonstration and made detentions in the city of Aktau and sporadic gunfire was heard in Kyzylorda, the Russian agency Sputnik said.
The unrest began in the country's far west as protests against a sharp rise in prices for liquefied petroleum gas that is widely used as vehicle fuel.
The protests then spread to the country's largest city, Almaty, where demonstrators seized and burned government buildings.
The military continued to guard the square adjacent to the burnt-out mayor's office, firing warning shots whenever passersby were slow to heed instructions to stay away.
Israel's foreign ministry said a 22-year-old Israeli citizen who had been living in Kazakhstan for several years was killed by gunfire on Friday night.
The protests in the Central Asian nation were the most widespread since Kazakhstan’s independence from the Soviet Union in 1991, with more than 4,400 people arrested.