After the meeting, Zelensky described the negotiations as "very productive".
Kazakhs went to the polls Sunday to elect their first new leader in 30 years following the departure of ex-president Nursultan Nazarbayev with his handpicked successor set for victory.
Career diplomat and interim president Kassym-Jomart Tokayev, 66, is running for the country’s ruling party with enthusiastic backing from Nazarbayev, who stepped down from the presidency in March.
The 78-year-old strongman’s departure shocked Kazakhs who had lived under his rule since Soviet times but he is still expected to call the shots in the oil-rich Central Asian state of 18 million people.
Tokayev has six rivals in the polls that open at 0100 GMT including one low-key opposition figure, but none are widely known in Muslim-majority Kazakhstan.
Tokayev, by contrast, has won endorsements from pop stars and film actors, and appears to have the weight of the state machine behind him.
Speculating on the outcome of the tightly-controlled vote, Tokayev’s campaign chief told journalists Friday that he predicted victory but without the overwhelming backing enjoyed by Nazarbayev.
“I think Tokayev will receive the support of the majority of the population, but to aspire to the figures that Nursultan Nazarbayev received would be inappropriate,” said campaign chief Maulen Ashimbayev in comments reported by Russian news agency Interfax.
One of the two Kazakh polling agencies permitted by authorities to operate in the run-up to the vote found Tokayev would win nearly 73 per cent of the vote.
Four years ago Nazarbayev scored nearly 98 per cent of a virtually uncontested vote where the official turnout was 95 per cent.
No Kazakh vote has ever been recognised as fully democratic by the Organisation for Security and Cooperation in Europe (OSCE), which has sent more than 300 observers to monitor this election.
– Transition ‘an illusion’ –
One of Tokayev’s first acts after taking over as interim president was to propose that the capital Astana — which Nazarbayev transformed from a steppe town into a million-strong city — be renamed “Nur-Sultan” in honour of his mentor.
The change went ahead without public consultation.
Many voters interviewed in the capital by AFP were unable to name any candidates except Tokayev.
“I will vote for him because I don’t know any of the others,” said 25-year-old Asya Seitbekova, who works for a private production company.
A taxi driver in Kazakhstan’s largest city and former capital Almaty, Timur Kozhabergenov, also said he would vote for Tokayev, calling him “the strongest candidate.”
The 43-year-old said he preferred “gradual change. Not like in Ukraine,” where comedian Volodymyr Zelensky has recently pushed out the previous president Petro Poroshenko.
“One day a stronger politician will emerge and displace Nazarbayev’s clan and that person will also get my vote,” he added.
There is only one openly opposition candidate in the race, journalist Amirzhan Kosanov, who has a track record of criticising the government.
However, he has come under fire for a lacklustre and tepid campaign where he has vaguely criticised the system, rather than attacking either Tokayev or his predecessor directly.
The buildup to the vote has been marked by an intensifying crackdown on the opposition which has seen courts sentence protesters to short stays in jail and police raid activists’ homes.
Human Rights Watch called the prospect of a genuine political transition “an illusion” and noted the persistence of rights abuses under Tokayev’s presidency.
“Kazakh authorities routinely break up peaceful protests, forcibly round up participants — sometimes literally binding their hands and feet — and sanction them with warnings, fines, and short-term imprisonment,” the watchdog said.
Nazarbayev’s foreign-based political nemesis, fugitive banker Mukhtar Ablyazov, has called for protests in cities across the country on Sunday and Monday.