The battle to reclaim Ukraine's occupied territories back from Russia is far from over, according to the country's foreign minister.

His comments come less than 24 hours after comedy actor Volodymyr Zelensky — who plays a fictional president in a popular TV show — thrashed incumbent Petro Poroshenko in the first round of presidential elections.

The two largely pro-EU candidates are set to go head-to-head in a run-off vote on April 21.

The presidential elections marked the first national vote since Russia annexed Crimea in early 2014 and subsequently supported an uprising by pro-Russian separatists in east Ukraine.

"We are not interested in having a frozen situation in Donbass because it is in the interest of Russia. We need to get Donbass back, but we need to get Ukrainian Donbass back to Ukraine," Pavlo Klimkin told CNBC's Steve Sedgwick in Kiev, Ukraine on Monday.

"I would not say that it should be the same patterns or the same model for Donbass and Crimea but we need to get back both occupied territories."

"It is a fundamental point of Ukrainian DNA," Klimkin said.