Relations between the two neighbours hit rock bottom before Hungary's 12 April election that saw Magyar beat long-time nationalist premier Viktor Orbán.
Hungary's incoming prime minister Péter Magyar offered on Tuesday to meet Ukrainian President Volodymyr Zelenskyy to "open a new chapter in bilateral relations" and address a long-running feud over the rights of Ukraine's ethnic Hungarians.
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Relations between the two neighbours hit rock bottom before Hungary's 12 April election that saw Magyar beat long-time nationalist premier Viktor Orbán.
Orbán, who was ousted after 16 years in power, had repeatedly used the central European country's veto power to stall financial assistance to Ukraine and block the country's EU membership.
"I am initiating a meeting with Ukrainian President Volodymyr Zelenskyy for early June, symbolically in Berehove, which has a Hungarian majority," Magyar said in a social media post after meeting the mayor of the Ukrainian city in Budapest.
"The purpose of the meeting is to help improve the situation of Hungarians in Transcarpathia and enable them to remain in their homeland," he added.
Ukraine's western Transcarpathia region is home to a sizeable ethnic Hungarian community.
Relations between Ukraine and Hungary soured in 2017 when Kyiv adopted a law mandating Ukrainian as the main language for secondary education.
Hungary said the law disenfranchised tens of thousands of ethnic Hungarians, who live mostly in Ukraine's westernmost region of Transcarpathia, part of the former Kingdom of Hungary until the end of World War I.
"The time has come for Ukraine to lift the legal restrictions that have been in place for more than a decade and for the Hungarians of Transcarpathia to regain all their cultural, linguistic, administrative and higher education rights, so that they may once again become equal and respected citizens of Ukraine," Magyar said.
"If we can resolve these issues, we can certainly open a new chapter in Ukrainian-Hungarian bilateral relations," he added.
Earlier in April, Zelenskyy travelled to the western region and met representatives of the Hungarian community there, and thanked them for their "resilience throughout this difficult winter and for supporting the front."
"Thank you for your service," he said in a post on X.
Unlocking crucial €90 billion for Ukraine
Late last week, the European Union gave final approval to a €90 billion loan for Ukraine after Hungary lifted its veto, ending a two-month long impasse caused by the Hungarian veto spearheaded by Orbán.
The breakthrough came two days after Zelenskyy announced that the Druzhba pipeline, which carries cheap Russian oil to Hungary and Slovakia, had been repaired and could resume operations.
The interruption of oil flows through Druzhba was at the core of Orbán's decision to veto the loan in February. The last-minute blockage outraged other EU leaders, who furiously condemned it as an "unacceptable" attempt to "blackmail."
Magyar, seen as a more moderate successor to Orbán, said he wanted a reset in relations with Brussels and would evaluate joining the eurozone.
He is also seen as less prickly towards Ukraine, saying he wants Hungary to have friendly relations with all of its neighbours.
He also stressed that Ukraine cannot be compelled to accept a peace deal that requires it to cede territory.
"No other country has the right to say that you should give up this or that territory. Anyone who says such a thing is a traitor himself," Magyar said.
But he also said Ukraine's EU accession "in the next ten years" would not be realistic and opposes any fast-track process for the country to join the bloc.