Mr Orban has been widely accused of flouting EU rules on democracy, civil rights and corruption since rising to power in 2010.
MEPs last week voted to bring disciplinary action against Budapest’s government by triggering Brussels’ Article 7 mechanism.
The dramatic move could see Hungary stripped of its EU voting rights, heaping further pressure on populist leader Mr Orban.
Senior German MEP Manfred Weber last night said EU leaders needed to discuss the controversy instead of dodging the issue.
Mr Weber, leader of the European Parliament’s centre-right European People’s Party (EPP) grouping, said: “The EPP invested more than two hours discussing Orban.
“But there have been zero minutes in the European Council, where EU leaders meet.
“France’s Emmanuel Macron, the Netherlands’ Mark Rutte and Luxembourg’s Xavier Bettel are all publicly complaining about Orban.
“They are attacking him, and defining themselves as his political opponents – but they don’t discuss it.”
The European Union’s 28 leaders, including Mr Orban, will meet at a high-profile summit in Salzburg, Austria on Wednesday.
But Brussels sources have said the Hungary issue is unlikely to be raised, as the talks will focus on migration and Brexit instead.
One EU diplomat said: “Orban will surely be around the table, but at this point he’s not on the table.”
Mr Weber called for dialogue with Mr Orban and said Hungary was not the only EU country breaching Brussels’ fundamental values.
He told the Financial Times: “The Czech Republic’s prime minister Andrej Babis says worse things about Muslims than Viktor Orban.
“Article 7 is not a Pandora’s Box. Europe needs to talk about these issues. It is a question of the survival of the western model.”
Mr Orban’s party described last week’s European Parliament vote as “petty revenge” and vowed to seek legal ways to challenge the ruling.
Poland and the Czech Republic have both vowed to back Mr Orban and veto any sanctions against the Hungarian government.