Magyar, who routed the nationalist Orban in Sunday’s election, said he made the call to Sulyok during a meeting to discuss convening the new parliament, expected in early May.
“I repeated to him that, in my eyes and in the eyes of the Hungarian people, he is unworthy of embodying the unity of the Hungarian nation, incapable of ensuring respect for the law,” Magyar told journalists after the meeting.
If the president refuses to step down, Magyar added, his government will introduce a law removing him and “all the puppets nominated to top posts by the Orban system”. He said the posts included the chief prosecutor and the head of the constitutional court.
He said the president, who is elected by parliament and has a largely ceremonial role, had responded “enigmatically” to the demand.
Magyar, 45, whose Tisza party won a two-thirds majority in the elections — giving the power to amend the constitution — said the new parliament would probably convene around May 6-7.
He said he had pushed Sulyok to set the earliest date possible. Orban met separately with the president who was to speak with all party leaders on Wednesday.
Magyar, a conservative who became an outspoken opponent of Orban’s rule, has vowed to bring in a “new era” and “regime change” that would roll back many of the actions taken by Orban and his Fidesz party to increase his control of state institutions and civil rights.
The government will make a priority of reforms — notably in justice and against corruption — that will help unblock billions of euros of European Union funds frozen by Brussels.
Magyar said he had invited several international leaders to visit Budapest for the 70th anniversary on Oct 23 of the 1956 uprising against Hungary’s pro-Soviet government at the time.
Orban, an ally of US President Donald Trump and Russia’s President Vladimir Putin, lost the elections after 16 years in power.
Trump had vocally endorsed Orban, but said Tuesday he liked Magyar, telling ABC News: “I think the new man’s going to do a good job — he’s a good man.”
Trump noted that Magyar was formerly a member of Orban’s party and said he had similar views on immigration, according to ABC News correspondent Jonathan Karl, who posted the remarks on X.
Magyar said Wednesday he welcomed Trump’s “very friendly” comments.