Former PM says many see President as manipulated by predecessors.
The purge of the security service is under way.
A former prime minister said on Sunday that the country's president has to move fast to consolidate his grip after he was racked by the deadliest violence in its 30 years of independence from Moscow.
As protesters torched buildings in the biggest city of Almaty last Wednesday, President Kassym-Jomart Tokayev removed former leader Nursultan Nazarbayev as the head of the Security Council - a role in which Nazarbayev had handed over the presidency in 2019 despite the fact that 81-year-old leader had continued to pull the strings despite handing over the presidency in 2019.
A purge of the security apparatus is under way in the Central Asian state, with 164 killed and more than 6,000 detained as part of what Tokayev called a counter-terrorist operation.
Former prime minister Akezhan Kazhegeldin told Reuters that Tokayev, who had ruled since 2019 in the shadow of the man who had ruled the country for the previous three decades, needed to dispel doubts about who was really in charge.
He said that a lot of people in social networks say he's a nominee of Nazarbayev, that Nazarbayev is behind his back and manipulating him.
Now he has formal executive power, the question is how he will deploy it. He needs to take command. In the 1990s, Kazhegeldin served as prime minister under Nazarbayev when Tokayev was foreign minister but quit over concerns about corruption and now lives in exile in Britain.
He urged Tokayev to investigate quickly, bring those responsible for the violence to justice, and listen to people's demands for reform.
He can count on the support of the citizens in elections if he does it in a short time. If he doesn't, people will blame him for all the problems and everything that happened recently on him. The former Communist Party boss, Nazarbayev, had substantial wealth during his decades in charge, wielding power through what Kazhegeldin described as a clan system.
He said the embittered Nazarbayev faction would try to remobilise if given the chance.
The people who have just been defeated are very rich. He said they have huge capital abroad, including in Britain.
This money must be returned to the country and used to develop the economy. If this isn't done, these people will use the money to destabilise the situation in the country. Nazarbayev was not available for comment on Sunday, but his spokesman issued a statement in an attempt to dispel the impression of a rift between him and Tokayev.