The three-man team is made up of Histadrut labor federation Chairman Ofer Eini, Agriculture Minister Shalom Simhon and Attorney Alon Gellert.
"Labor has certain demands when it comes to economical, social and security issues, as well as other requirements stemming from its political path and stances," said Barak's office. "Deliberations on these issues have yet to be exhausted and seeing eye to eye on them is pivotal to an agreement.
"(Israel) need a unity government and not a narrow right-wing one. We call on Kadima to begin negotiations as well."
Barak is attempting to shape his interests ahead of the party's Tuesday conference, meant to discuss its possible teaming with Prime Minister-designate Benjamin Netanyahu's government.
The Labor chair would like to present members of his party with a full-fledged coalition agreement, or at least with an extensive draft of one, so not to waste any time. Presenting the party with a de facto agreement would undoubtedly pressure them into approving it.
Seven Labor Knesset members who are opposed to the party joining a Likud-led government issued a statement later in the day, saying that "the appointment of the coalition negotiation team without the approval of the party's institutions is something which has never been done before.
"This move is breaking the party's democratic rules of the game and an attempt to force an established fact on the Central Committee members."
Those who have sided with Barak so far include Minister Simhon, Infrastructure Minister Binyamin Ben-Eliezer, Knesset Members Orit Noked and Matan Vilnai and Ofer Eini. One pivotal vote missing so far is that of Social Affairs Minister Isaac Herzog, who is said to still be deliberating the question.