Reaction has been swift after European Parliament President Martin Schulz announced he would not be seeking a third term as the assembly's leader.
Instead, he will run in next year's German elections in the hope of winning a seat in the Bundestag.
S&D group Chair Gianni Pittella praised Schulz, saying he had "upgraded" the role of Parliament President during his time in office.
Pittella and his socialist MEPs are insisting that the next President, due to take up office on 1 January, must come from their political grouping otherwise, they aregue, all three EU institutional presidencies - Parliament, Council and Commission - could be held by people aligned to the centre-right EPP grouping.
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The S&D group had thrown its weight behind Schulz staying on for another term, saying this was particularly necessary when the EU faces problems on various fronts, including the migration crisis and Brexit.
Belgian S&D group MEP Marc Tarabella said Schulz had been "a remarkable President, probably the most efficient in years", adding that he had "overcome political cleavages to become the President of all Europeans."
EPP group leader Manfred Weber said in a press point on Thursday that his group would be announcing a candidate to replace Schulz in December, and declined to say whether he would be in the running himself.
He said his priority would be to "talk to all the groups so we can exclude extremist groups from influence and exclude them from having a voice in appointments", adding that the focus would be on "finding a consensus candidate."
Austrian EPP group member Paul Rübig said, "Schulz will move more European thinking into German decision making."
ECR group Chair Syed Kamall said Schulz's departure was an opportunity for Parliament to "rethink entirely how it is being run and for the EPP and S&D groups to seriously ask if the grand coalition [Schulz] leads has been healthy for democracy and transparency.
"For the past 30 months, decisions about the future of the EU have been made by five men from four 'old' EU states stitching-up every major issue, and with the Socialists getting their way more often than not. With the figurehead of the European Parliament's backroom dealing now leaving, the grand coalition should seriously ask if its conduct is increasing or undermining people's perceptions of the European Parliament."
Helga Stevens, the ECR group candidate for the presidency, said, "Nobody can deny that Martin Schulz has propelled the Parliament into the forefront of EU decision-making. However, where he failed was in concentrating that power and influence in the hands of just a few men rather than in the hands of all 751 MEPs who collectively represent the plurality and diversity of European voters.
"Decisions about the future of the EU should be made by all 751 MEPs in open debate, not by three men from the Parliament meeting with two men from the Commission in a hotel backroom.
"With Martin Schulz now leaving the Parliament we have an opportunity to change how the institution is run so that every voice matters and all MEPs can finally have a say in the future of our European Union. We can see a true cultural change in how the European Parliament works that will restore people's faith in the Parliament as a forum of open debate and noble causes, not of backroom dealing. "
UK Tory MEP Charles Tannock told this website, "President Schulz, although coming from a very different political family and outlook to mine, has been an excellent Speaker of the Parliament and has been very helpful to me as an MEP when I have asked for his help, even on matters probably not to his immediate political interest, such as meeting religious leaders I have hosted in the Parliament as my guests. I wish him the very best for his future."
Meanwhile, ALDE group leader Guy Verhofstadt tweeted:
Ukip deputy Margot Parker said of Schulz, "He wanted to bully and manipulate people into giving him a third mandate but even he eventually gave up the power grabbing. The fact a third term was considered shows what a banana republic this place is."
Giles Merritt, founder of the Friends of Europe think tank, said, "If Martin Schulz were to become Germany’s foreign minister, it would be very good to see a wider EU perspective informing Germany’s foreign policy."
Former MEP Andrew Duff commented, "Martin has been a good President of the House in many ways, advancing its standing and improving its efficiency.
"But it’s good that he’s going now: a third term as President would have been bad for the institution and for himself. There needs to be a real contest now for his successor as the Parliament comes to terms with the possibility of the further disintegration of Europe.
"A new constitutional moment is upon us, and for Parliament just to be pragmatic will not be enough."
Denis MacShane, a former Europe Minister in the UK, told this website, "Schulz has been the most energetic President of the Parliament in decades and has put the institution on the map. He has tried to uphold Social Democratic values at a time when they are coming under attack from all sides. I hope MEPs in choosing his successor realise what a negative signal it would be if the EPP had the total monopoly on all top EU presidency posts."