"It will take time until we succeed in bringing forth a leader in whom the public can trust and support," said coalition chairman Knesset Member Avigdor Itzchaky (Kadima).
Itzchaky is known for his internal opposition of Prime Minister Ehud Olmert and has repeatedly been suspected of considering a return to his former party, Likud.
Although he conceded that Olmert had been the "most acceptable" candidate during election time, he emphasized that the situation had changed and worried that his party was "not adequately preparing the next generation of leaders."
"I understand public sentiment that feels that we're in the largest leadership crisis ever since its inception," he added, expressing his opinion that his party is unable to advance with its current leadership.
His words constitute another blow not only to Olmert, but also to other politicians in Kadima, who are vying for control of top positions.
Among these politicians is presidential hopeful Shimon Peres. Itzchaky censured the "Peres bill", which calls for open ballot presidential elections, saying that such an election would not represent public opinion, but rather a coalition agreement.
Itzchaky also mentioned the recent trial of former justice minister Haim Ramon, in particular, and criminal charges against politicians in general.
"We need to check and ensure that politicians are the best and most appropriate people for the job," he said. "Candidates for prime minister should be examined by the Fraud Investigation Unit prior to elections."
However, the coalition leader doesn't believe that other parties necessarily offer a better alternative. "The solution is not to bring someone we disliked in the past, (Opposition Leader Benjamin) Netanyahu, for example," he said.
Regarding the Labor Party, he conceded that Peretz is still in charge and should not be forcibly ousted, but expressed his personal support for MK Ami Ayalon in the upcoming Labor primaries in May.