In his speech in front of MPs, officials and foreign dignitaries, Zelenskiy said his election showed people were exhausted of an exploitative political class and told lawmakers who weren't ready to change things they should resign.
After the meeting, Zelenskiy's adviser Andriy Bohdan said that the decree on disbanding the parliament will be signed "in the nearest future" and "it is most likely" that snap parliamentary elections will be held on July 21.
During his speech at the inauguration ceremony on Monday, Zelensky said he would dissolve Verkhovna Rada (Ukrainian parliament).
Volodymyr Zelensky is the Ukraine's youngest post-Soviet president.
A Kremlin spokesman said last Thursday that Moscow was not aware of "any plans on possible contacts" between President Vladimir Putin and Zelensky following the inauguration.
The next parliamentary polls in Ukraine had been scheduled for October.
Zelenskiy won a landslide election in late April with 73% of the vote, defeating the incumbent President Petro Poroshenko as he rode a wave of popular dissatisfaction with Ukraine's political class and weariness over five years of war.
Zelenskiy arrived at his inauguration Monday after walking through Kiev's Mariinsky Park, where cheering supporters thronged barricades marking his path to the parliament building.
Ukraine's new President Volodymyr Zelensky used his inaugural speech on Monday to announce a snap election, before promising to end the country's five-year conflict with Russian Federation.
Defence Minister Stepan Poltorak and the head of the SBU security service Vasyl Grytsak swiftly tendered their resignations.
At the U.N. Security Council on Monday, Russia failed to get enough support to convene a meeting over a decision by Ukraine's parliament last week that grants special status to the Ukrainian language and makes it mandatory for public sector workers.
Dressed in a dark suit, he exchanged high fives with supporters waiting outside, took selfies with them and even jumped up planting a kiss on a supporter's forehead.
On Friday, several parties in Ukraine's ruling coalition broke apart, a move that gives them an extra 30 days to form a new coalition.
"The legally dubious decision to disband parliament will certainly be contested in court but Zelensky has shown that it is going to be him who will lay down the agenda and that he will dominate the political landscape".
Hours after Zelenskiy was sworn in, Prime Minister Volodymyr Hroysman said he will resign on May 22 and suggested that he will run in the snap elections. If accepted, he would remain as acting prime minister until after the elections.
Groysman, also 41, praised the work of his government over the past three years.
"We didn't start this war but it is up to us to end it", he said. "But we need to be the one to finish it".
Ukrainian President Volodymyr Zelenskiy exits the parliament after his swearing in as Ukraine's sixth president since its independence in 1991, on May 20, 2019 in Kiev, Ukraine.
Addressing the people of Ukraine, Zelenskiy finished his inaugural speech by saying, "All my life I tried to do all I could so that Ukrainians laughed". "In the next five years, I will do everything, Ukrainians, so that you do not cry".