Barak spoke during a Labor Party get-together held at the home of Knesset Member Danny Yatom.
"The plan was to hold an informal gathering ahead of the opening of the Knesset's spring session," the host told Ynet. "The atmosphere was pleasant. We sat for more than two hours.
"I said that it was going to be a critical and stormy session, and that I believe the prime minister should not be supported, that he should have resigned after the Second Lebanon War.
"Now, with all the suspicions against him, the public's trust in him has been completely shattered. Since the public cannot be replaced, the prime minister must be replaced," Yatom said.
Barak, on his part, reiterated his estimate in regards to the elections. He added, "Once people wouldn't take us seriously when we made these remarks, but today it has become increasingly clear that this will be the date of the elections."
Yatom noted that Barak "also said that there is no reason to rush and that we should keep cool."
Meanwhile, several of Kadima's MKs met Friday for what was dubbed a "conceptual forum". MK Isaac Ben-Israel hosted the meet at his Ramat Hasharon home, but stressed that the get-together was "not an attempt to stage a coup, or shift our political support… We just want to devise ways to push Kadima's agenda forward."
Behind the scenes, senior members of the ruling party are preparing for possible primaries.