Parliament's EPP group leader Manfred Weber has said the UK is "descending into chaos" and warned that the "clock is ticking" on its decision to leave the EU.
Speaking in Strasbourg on Tuesday, the German MEP reacted to the outcome of last week's election in the UK which resulted in a hung parliament by telling reporters, "London is sinking into chaos and the stability that Theresa May sought in calling the early election has not come about.
"Unfortunately, the UK will clearly not have more instability and the election result will also have negative consequences for the Brexit talks."
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Weber also attacked plans by the Tories to enter into an informal agreement with the DUP, adding, "The Brexit negotiations will need a wide and major consensus and the DUP will not be a good source of advice and should therefore not be allowed to be involved."
On the Brexit process, Weber said, "Time is marching forward and it is in the interests of the UK to come together as soon as possible."
Speaking separately, S&D group Chair Gianni Pittella also poured scorn on Theresa May, saying, "She thought she was going to win big but she did not need an election. She now finds herself having to form a government with an extreme right wing organisation. It is all inexplicable."
The Italian MEP, also addressing a news conference, said, "The UK voters did well to punish May's attitude but, when it comes to the Brexit discussion, we in the EU are ready to start talks tomorrow. We are ready."
On speculation that Labour and Tory MPs in the UK are in talks about securing a soft Brexit, Pittella said, "We were never in favour of a hard Brexit. I prefer to talk about a fair Brexit, not a soft or hard Brexit, but one that recognises the rights of EU citizens in the UK and UK citizens in Europe and where the UK pays what it is committed to paying."
Pittella also said he would speak on the phone to UK Labour leader Jeremy Corbyn later on Tuesday and invite him to a Socialist group plenary meeting.
Further comment on the British election and Brexit came from ALDE group leader Guy Verhofstadt, who is Parliament's Brexit negotiator.
The Belgian deputy said one of the priorities in the talks will be that the UK can still take part in schemes like Erasmus, which marked its 30th anniversary on Tuesday.
He told a news conference, "After the election we continue to await the UK position on Brexit as it is unclear if the government will stick to its original line or change it, taking into account the outcome of the election last week.
"From our side, we welcome a very close relationship in the future with the UK and prefer a Norway style relationship. But we have also indicated we will not compromise on certain conditions, including a fair financial settlement.
"Parliament believes the Good Friday agreement is a key priority and to avoid a hard border. This is even more important as the Tories are it seems now trying to secure an agreement with the DUP."
The MEP added, "We have to understand that this is not about the Tories leaving the EU but the UK leaving the EU so we need to start these talks soon. We need to see clarity in the coming days because the uncertainty cannot continue."
He went on, "Talking about Brexit has paralysed the EU. We have not reformed or changed because we have been busy with the UK decision. This has to change now. One of the outcomes of the UK election was that the public do not support a hard Brexit. It is up to the UK government to accept responsibility for this."