Orban, who is an outspoken critic of military aid to Ukraine and has the warmest relations of any European Union leader with Russian President Vladimir Putin, held talks with Zelenskiy during his first trip to Kyiv in more than a decade.
In brief joint statements to reporters after the talks, Orban said he valued Ukraine's push to promote Zelenskiy's vision of peace at an international summit in June in Switzerland and its aim to hold a second, follow-up summit later this year.
"I asked the president to think about whether we could reverse the order, and speed up peace talks with making a ceasefire first," Orban said.
"A ceasefire connected to a deadline would give a chance to speed up peace talks. I explored this possibility with the president and I am grateful for his honest answers and negotiation."
Zelenskiy, who spoke before Orban, did not respond to those comments.
My first trip after assuming the Presidency of the Council of the EU led me to Kyiv for a meeting with President — Orbán Viktor (@PM_ViktorOrban) @ZelenskyyUa. I assessed the possibility of a deadline-bound ceasefire, that could provide an opportunity to speed up peace negotiations. I will report my findings to… pic.twitter.com/TqPeDAvsoeJuly 2, 2024
The Ukrainian leader's foreign policy adviser, Ihor Zhovkva, later said in televised remarks that it was not the first time a ceasefire had been proposed and that Zelenskiy had responded to Orban with his publicly known stance.
He did not elaborate but officials in Kyiv have often said Russia would use any let-up in fighting to regroup and strengthen itself for another, even larger attack on Ukraine.
In his statement to reporters, Zelenskiy touted the possibility of a broad bilateral co-operation agreement between Ukraine and Hungary.
"The content of our dialogue today on all issues can become the basis for a bilateral document between our states, a document that will regulate all our mutual relations," he said.
Today, Prime Minister Viktor Orbán — Volodymyr Zelenskyy / Володимир Зеленський (@ZelenskyyUa) @PM_ViktorOrban and I discussed the most fundamental issues of our neighbourly relations – trade, cross-border cooperation, infrastructure, and energy.We also talked about the humanitarian sphere – everything that affects the lives of our… pic.twitter.com/6PQzFqWtYwJuly 2, 2024
Welcoming Zelenskiy's comments, Orban said Hungary would like to help in modernising Ukraine's economy.
Ties between the neighbours came under heavy strain after Russia launched its full-scale invasion of Ukraine on February 24, 2022, with Hungary often opposing EU efforts to support Ukraine.
Under Orban, who upset some EU countries by holding talks with Putin last October, Hungary has repeatedly accused Ukraine of curbing the rights of about 150,000 ethnic Hungarians living in the far west of Ukraine.
Ukraine, meanwhile, is keen to secure Hungary's backing as it relies heavily on financial and military support from the 27-member EU, where unanimity is needed for many decisions.
Orban linked Tuesday's surprise Ukraine visit to Hungary having assumed the six-month rotating presidency of the European Council on Monday.
"The aim of the Hungarian presidency is to contribute to solving the challenges ahead of the European Union. That's why my first trip was to Kyiv," Orban wrote on Facebook after he arrived in Kyiv.
Last week, the EU opened formal membership talks with Ukraine at its summit in Brussels, giving Ukraine a morale-lifting boost, although a long and tough road still lies ahead before it can join the bloc.
Zelenskiy and Orban were filmed on the sidelines of that summit in what looked like an emotional exchange.
Ukraine has denied Hungary's assertion that it is restricting the rights of Hungarian speakers in western Ukraine but says it is open to addressing any concerns.
Ukraine passed a law in 2017 that required all schools to teach students over the age of 10 in the Ukrainian language.
Hungarian officials saw this as a breach of the ethnic Hungarian minority's rights.
Some changes were made in December 2023 when the issue became critical for Ukraine's EU accession talks.
Hungary said the changes were an improvement but did not go far enough.
