Mr Zelenskiy, 41, became famous nationwide for his comic portrayal in a Ukrainian TV series of a high school teacher who becomes president after a video rant against corruption goes viral. Russian Federation seized Crimea in 2014 in a move that Ukraine and nearly all of the world views as illegal. Both candidates have pledged to keep the country on a pro-Western course.
But he has been coy about exactly how he plans to achieve all that and investors want reassurances that he will accelerate reforms needed to attract foreign investment and keep the country in an International Monetary Fund program.
But a victory for Zelenskiy in Sunday's second-round runoff would nonetheless be a dramatic departure in a country where previous presidential elections since independence were won by experienced politicians including three former prime ministers.
A voter casts her ballot at a polling station during the second round of a presidential election in Kiev, Ukraine April 21, 2019.
Ukraine, with a population of 42 million, is the least-trusting electorate in the world.
"I don't think it would be in the interests of our bilateral relations to follow the path of non-recognition of these elections and thus closing the doors to contacts with Ukraine's new authorities", Kosachev told Russiya-24 TV channel.
Although he instituted some reforms, critics said he had not done almost enough to curb the country's endemic corruption.
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"Russia values the existence of the DPR and LPR [the self-proclaimed Donetsk and Lugansk People's Republics - TASS] because they keep Ukraine from joining North Atlantic Treaty Organisation and the European Union", Chesnakov pointed out.
Kyiv's pursuit of closer ties with the West and the European Union was the trigger for Ukraine's ongoing conflict with Russia, which developed into a war along the border that culminated with the controversial annexation of the Crimean peninsula, as well as Russian incursion into Ukraine's separatist eastern provinces in 2014.
At stake is the leadership of a country on the frontline of the West's standoff with Russia following Moscow's annexation of Crimea and support for a pro-Russian insurgency in eastern Ukraine.
The first-time candidate, who stars in a TV sitcom about a high school teacher who becomes president nearly by accident, appeared to have won in both the west and the east, a rarity in post-Soviet Ukraine.
Zelenskiy remains something of an unknown quantity and faces scrutiny over his ties to a powerful oligarch who would like to see Poroshenko out of power.
"The most important" thing is to "stop the fighting", Zelensky said, also promising to bring back Ukrainians held in rebel areas or in Russian Federation that Kiev says are political prisoners or prisoners of war.
"These people are much more keen to talk up Ukraine's achievements over the past five years: there's visa-free travel to Europe, there's been sweeping banking-sector reform, there have been anti-corruption institutions put in place - although they're not working very well", he added. "Thanks to all the Ukrainian citizens who voted for me, and to all who didn't: I promise I won't mess up".