"We have taken the first step," said Zelensky, adding that "now we have to take the rest".
Zelensky, a former TV comedian who shot to the presidency in the April elections, wanted to make progress with the Minsk Accord an international peace effort aimed at putting an end to the ongoing conflict between Ukraine's Army and pro-Russian insurgents in the country's eastern regions known as the Donbass.
The war, which erupted in 2014 - coinciding with Russia's annexation of Crimea - has claimed the lives of over 10,000 people.
Earlier, Zelensky headed to Borispol airport outside the Ukrainian capital, Kiev, to meet the freed prisoners returning from Russia, among them 24 sailors detained in November 2018 when Russian Coast Guards impeded the passage of three Ukrainian naval vessels through the Kerch Strait, which links the Black Sea and the Sea of Azov.
Also touching down on Ukrainian soil was filmmaker Oleg Sentsov, who was sentenced to 20 years in prison by the Russian judiciary in 2015 for supposedly carrying out terror plots, according to Efe news.
Sentsov, whose imprisonment was widely regarded as political, was awarded the European Union's Sakharov Prize in 2018.
Russian President Vladimir Putin did not make an appearance at Vnukovo international airport, where a plane carrying the 35 prisoners released from Ukraine touched down.
Instead, they were welcomed by Russia's Human Rights Commissioner Tatyana Moskalkova.
There are currently no direct charter flights between the neighbouring nations.
One of the key figures released by Ukrainian authorities was Volodymyr Tsemakh, who investigators consider a key suspect in the 2014 downing of MH17.
The Dutch-led Joint Investigation Team has accused Russian-backed rebels of bringing down the passenger plane with a Buk missile transported across the Ukraine-Russia border. Moscow has repeatedly denied any involvement in the incident.
The downing of the plane over the Donbass killed 283 passengers and 15 crew and sparked a huge international outcry.
Also among the Russian detainees in the swap was Kirill Vyshinsky, a journalist and former Director of Russia's RIA Novosti Ukraine branch, according to the head of the Rossiya Segodnya, Ria Novosti's successor.
He was arrested in 2018 accused of treason.
Russia's Foreign Ministry said the swap was a "very important step" and called on both sides to work to resolve their bilateral crisis.
( With inputs from IANS )