Nearly 6,000 people, including a number of foreigners, have been arrested in Kazakhstan over the riots that have shaken Central Asia's largest country, the presidency said on Sunday.

The energy-rich nation of 19 million people has been rocked by a week of upheaval with dozens killed.

In total, 5,800 people have been detained for questioning as part of 125 separate investigations into the unrest, the presidency said in a statement.

The figures included "a substantial number of foreign nationals," it said without elaborating.

"The situation has stabilised in all regions of the country," even if security forces were continuing "cleanup" operations, the statement added after President Kassym-Jomart Tokayev held a crisis meeting. 

Fuel price rises sparked the unrest that broke out a week ago in western provincial areas but quickly spread to large cities, including the economic hub Almaty, where riots erupted and police opened fire using live rounds.

The interior ministry, quoted Sunday by local media, put property damage at around €175 million.

More than 100 businesses and banks were attacked and looted and more than 400 vehicles destroyed, the ministry reportedly said.

A relative calm appeared to have returned to Almaty, with police sometimes firing shots into the air to stop people approaching the city's central square, an AFP correspondent said.

Supermarkets were reopening on Sunday, media reported, amid fears of food shortages.

Kazakhstan said Saturday its former security chief had been arrested for suspected treason, as Russia hit back at US criticism of its deployment of troops to the crisis-hit country.

News of the detention of Karim Masimov, a former prime minister and longtime ally of Kazakhstan's ex-leader Nursultan Nazarbayev, came amid speculation of a power struggle in the ex-Soviet Central Asian nation.

The domestic intelligence agency, the National Security Committee (KNB), announced that Masimov had been detained on Thursday on suspicion of high treason.

President Tokayev sacked Masimov after protests turned into widespread violence, with government buildings in Almaty stormed and set ablaze.

Masimov, 56, was fired at the height of the unrest on Wednesday, when Tokayev also took over from Nazarbayev as head of the powerful security council.

Nazarbayev's spokesman Aidos Ukibay on Sunday again denied rumours the ex-president had left the country and said he supported the president.

In a hardline address to the nation on Friday, Tokayev said 20,000 "armed bandits" had attacked Almaty and authorised his forces to shoot to kill without warning.

Much of the public anger appeared directed at Nazarbayev, who is 81 and had ruled Kazakhstan since 1989 before handing over power.

Many protesters shouted "Old Man Out!" in reference to Nazarbayev, and a statue of him was torn down in the southern city of Taldykorgan.

Critics accuse him and his family of staying in control behind the scenes and accumulating vast wealth at the expense of ordinary citizens.

The full picture of the chaos has often been unclear, with widespread disruptions to communications including days-long internet shutdowns.

Flights into the country have been repeatedly cancelled and Almaty's airport will remain closed "until the situation is stabilised", authorities said Sunday.

According to the interior ministry 26 "armed criminals" had been killed in the unrest. Eighteen security officers also died and more than 740 were wounded. 

Tokayev has thanked thanked the Moscow-led Collective Security Treaty Organisation (CSTO) for sending troops to help deal with the unrest.

The CSTO has been dispatching several thousand troops to Kazakhstan, including Russian paratroopers, who have been securing strategic sites

Tokayev says the deployment will be temporary, but US Secretary of State Antony Blinken warned on Friday that Kazakhstan may have trouble getting them out.

"I think one lesson in recent history is that once Russians are in your house, it's sometimes very difficult to get them to leave," Blinken told reporters.

Tensions between Moscow and the West are at post-Cold War highs over fears of a Russian invasion of Ukraine, with talks between Russia and the US to take place in Geneva on Monday, after a working dinner on Sunday evening.

Russia has ruled out any concession at the talks.

"We will not agree to any concession. That is completely excluded," Deputy Foreign Minister Sergei Ryabkov said Sunday.

"We are disappointed with the signals coming in the last few days from Washington but also from Brussels."