Nazarbayev, 78, who holds the official title of Yelbasy, or national leader, and continues to run the ruling Nur Otan party, has routinely taken over 90 per cent of the vote in elections described by Western observers as neither free nor fair.
Responding to a question from Al Jazeera during a news conference, Tokayev said he had advised law enforcement agencies to be "tolerant and to exercise restraint" with protesters, but added that any serious violations of Kazakhstan's laws "would not be tolerated".
Image copyright Reuters Image caption Kassym-Jomart Tokayev is widely expected to win What is the background?
The snap presidential election in Kazakhstan ended on June 9 with the voter turnout of 77.4%.
Sunday's vote was marred a police crackdown on protesters who took to the streets against what they see as a mockery of democracy. Sunday saw hundreds of arrests after the biggest protests in Kazakhstan in at least three years, as demonstrators urged a boycott of what they said was a fixed election.
Monitors from Organisation for Security and Cooperation in Europe (OSCE) said "a lack of regard for fundamental rights, including detentions of peaceful protestors, and widespread voting irregularities on election day, showed scant respect for democratic standards". He was the speaker of the Senate before having been appointed interim president following Nazarbayev's resignation.
That decision, which went ahead without public consultation, fuelled disillusionment with Kazakhstan's government.
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Ivan Sedov, a 42-year-old entrepreneur from Almaty said he had voted for Daniya Yespayeva, 58, the only woman on the ballot "in the spirit of protest".
A continued role for Nazarbayev in the government will likely overshadow any transition of power. I think it has been rushed through. There was only one candidate who was openly in opposition in the race, journalist Amirzhan Kosanov, who has criticised the government.
However, even his criticism has been vague, rather than directly attacking either Tokayev or Nazarbayev.
Protesters have been sentenced to short stays in jail and police have been raiding activists' homes, according to AFP.
Human Rights Watch called the prospect of a genuine political transition "an illusion" and noted the persistence of rights abuses under Tokayev's presidency.
Nazarbayev's foreign-based political nemesis, fugitive banker Mukhtar Ablyazov, called for protests in cities across the country on Sunday and Monday.