Mr Kucuk, head of the UBP has been making a series of contentious decisions since the elections.
Earlier this week he arbitrarily removed two MPs from his UBP party. He has also changed his mind on resignation yet again.
His current stance is that he will carry on as party leader until the membership agree on a single candidate to replace him.
Supporters of the two sacked MP’s were protesting outside the UBP head office this week but were harshly criticised by Mr Kucuk. He said that he would not tolerate such lack of party discipline.
Yesterday, one of the sacked MP’s Sunat Atun, the MP for Famagusta held a press conference in front of UBP head office in Nicosia.
He produced a petition signed by UBP members in Famagusta and Nicosia. It demanded that Mr Kucuk resign immediately.
Mr Atun reminded the press that he was arbitrarily dismissed even though he had one the most votes of any UBP MP. He also reminded the press that Mr Kucuk had been voted out of his constituency.
He said that it did not make sense for Mr Kucuk to be talking to other parties about forming coalitions in parliament when he himself could not enter there.