In a joint declaration, parliament group leaders Joseph Daul, Hannes Swoboda and Guy Verhofstadt last week said that the next elected commission president would be "the result of a transparent process, not the product of back-room deals".
But GUE/NGL president Gabi Zimmer criticised the statement, arguing that it is undemocratic and that "striking deals amongst themselves belongs to the past".
"The parliament will change considerably after the elections and it would be appropriate that these three groups finally realised that.
"Contrary to what they say in their statement, these are backroom deals between three groups in the European parliament, and we object to them," she said.
According the joint statement, the ALDE, EPP and S&D groups will each present their own candidates for the position of commission president, from which the successful candidate will be chosen.
It continued, "The next commission president must be chosen from amongst them. Citizens' expectations will thereby be respected, making the European Union more democratic and closer to them."
However, Zimmer protested, "These elections were supposed to change the way the commission president was selected and make it a more democratic system and one in which the EU electorate would have a real say."
"These decisions should be taken in an open and transparent way involving all the political groups and reflecting the composition of the new parliament.
"EPP, S&D and ALDE group leaders cannot think that they can carry on as before, concluding undemocratic agreements behind closed doors and expecting MEPs to ratify them," she insisted.
Meanwhile, Greens/EFA co-chair Rebecca Harms and president of the Green party Monica Frassoni also responded, saying, "This deal between the three major groups confirms what was widely expected: in spite of all the promises that these elections would fundamentally change the way the European commission president is chosen, they want to defend as much as possible their tradition of striking deals among themselves.
"They want to make sure that the status quo prevails, dividing up the spoils between themselves ahead of the elections," stressed the pair.
"The Greens are campaigning for real change in the context of the forthcoming elections," they added.
"We believe the European elections should be the democratic foundation for the coming legislative term and are strongly opposed to political deals being concluded before European voters have had their say.
"We refuse to continue with business as usual."