Olmert made the remarks in Tel Aviv's Exhibition Grounds, where Kadima members gathered to celebrate their election victory and make a toast ahead of Passover.
Turning his attention to coalition negotiations, the acting PM said: "We didn't come to play and pull tricks. We don't want to hurt any body, there is no leader we disqualify, and we'll respect everyone."
"Perhaps for a short time there was the impression or illusion that someone else may be able to form the government," Olmert said, referring to attempts by Labor party leader Amir Peretz to join forces with right-wing parties. "I’m glad things are clear now. We're not aiming to argue or disparage or engage in a confrontation with anyone."
Referring to talks with other parties on joining the coalition, the acting prime minister said the offers made to the various parties were "honest."
Olmert added Kadima was formed to offer a different kind of politics, after learning from the mistakes of the past. He said Kadima would aim to advance the kind of rule that is "cleaner, more devout, and knows to make the right distinctions."
The Kadima leader thanked all party activists and volunteers, as well as ailing Prime Minister Ariel Sharon, who set up the party in November 2005.
Olmert addresses Kadima activists (Video: Yaron Brenner)
"In the last days before the elections and on the night after them I prayed for a miracle, that he would open his eyes even for one evening, so we can tell him – Arik, your dream came true," Olmert said.
"I'm certain that in some way, there in the quiet room, Arik hears and Arik knows, and God willing we'll be proven right," Olmert concluded.