Others, however, want stronger action. Like throwing Fidesz out of the EPP grouping altogether.
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A prominent Hungarian MEP, Tamás Deutsch, has been sanctioned by his own political group in the European Parliament.
It comes after he insulted the chairman of the European People's Party (EPP), Manfred Weber.
At the end of November, Deutsch accused the German MEP of using the language of the Gestapo over Hungary adhering to the EU’s rule of law mechanism.
During a Hungarian TV show, he said: "I want to react on Manfred Weber’s statement without offending any of you here. He says if you have nothing to hide, you should not be afraid. I remember well, the Gestapo and (communist secret police) AVO used the same words: 'If you have nothing to hide, don’t be afraid'."
The EPP has stripped Deutsch of the right to hold a position within the group or speak on its behalf in the European Parliament.
Deutsch apologised to Weber twice. But for many members, this scandal is another reason to remove Hungary’s ruling party, Fidesz, from the EPP grouping.
One Polish MEP recalled the recent sex scandal of another Fidesz MEP, József Szájer.
"Well, I personally have nothing against people going to gay orgies or doing drugs in their free time. But we are somewhat tired of the hypocrisy of pretending Christian democrats and all this family stuff and this double life," Polish MEP Radek Sikorski (EPP) told Euronews.
EPP said it will decide on the continued membership of Fidesz once the health crisis is over.