With the vote, the EP endorsed the report of Green MEP Judith Sargentini, which said recent developments in Hungary represent a systematic threat to democracy, the rule of law and fundamental rights in the country and constitute a clear risk of a serious breach of European Union values.
"All my solidarity. No to sanctions and to trials of freely elected governments", read the post by Salvini, who is also Italy's Deputy Prime Minister.
Mitsotakis's party, New Democracy, is in the same conservative bloc in the European Parliament as Orban's, the European People's Party (EPP).
But it was still unclear whether the 751-strong European Parliament would be able to muster the two-thirds majority needed to pass the censure motion, which accuses Hungary of breaching core EU values.
"We expect Viktor Orban.to make clear that he is prepared to recognize in Hungary the concerns that are being expressed in Europe and act accordingly", Manfred Weber, head of the EPP's parliamentary group, told Germany's ZDF television.
If the resolution is adopted, it will be the first time that the European Parliament takes the initiative for such a procedure, though it has backed an Article 7 action taken against Poland, triggered in December 2017 by the European Commission.
The experts called on Hungary to "refrain from engaging in practices that are threatening fundamental civic freedoms, in particular, the right to freedom of expression, peaceful assembly, association, as well as the principle of non-refoulement and the ban on incitement to hatred and discrimination", and encourages European institutions to continue applying pressure on the Hungarian government.
The European Parliament will vote next week on a proposal to trigger Article 7 against Hungary. "You think you know better than the Hungarian people what the Hungarian people need".
But Weber, a close ally of Merkel, also spoke of "building bridges" with Hungary and noted the EU's failure to take action in a similar rule-of-law case against Poland.
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Dutch anti-Islam campaigner and MP Geert Wilders described the vote on Twitter as "a bloody shame".
The MEP said Hungary was going to challenge the vote in the parliament - an issue that could end up at the EU's top court.
"I have always been in favour of building bridges and I want to continue to do so, but yesterday (Tuesday) I didn't see any readiness from the Hungarian PM to make a move towards his European Union partners and address our concerns", Mr Manfred tweeted.
"Democracy in our member states and in our European Union can not exist without the rule of law", Timmermans said, and went on to list concerns about fundamental rights, corruption in Hungary and the treatment of migrants.
One of the biggest sticking points, however, is the response to the European migrant crisis by the Hungarian government, which has refused to participate in an EU-wide refugee relocation scheme.
Although Orban's Fidesz party is part of the EPP, several of the lawmakers voted against their Hungarian allies.
"The order has arrived from Berlin and they will vote accordingly", Orban said, in reference to German Chancellor Angela Merkel, whose governing Christian Democratic Union is the largest party in the EPP.
In June, Hungary's parliament overwhelmingly passed a law imposing jail terms for anybody seen to be aiding undocumented immigrants.