Sharon now heads a minority government.
The prime minister's office said Sharon phoned Torah Judaism Knesset Members Yaakov Litzman and Moshe Gafni and invited them for talks.
The Labor Party Tuesday formally agreed to coalition negotiations, and its representatives are also supposed to meet Sharon Sunday.
Thursday, July 22, Sharon is to meet Shas' political leader Eli Yishai.
Sharon could have a comfortable majority, supportive of his plan to withdraw from the Gaza Strip and the northern West Bank, if he could co-opt Labor.
However that is not popular in his Likud Party. His hawkish National Religious Party coalition partner is likely to quit if Labor joins, and he would be left with secular coalition parties only, a prospect that is not popular in the Likud.
His ardently secular Shinui partner opposes a coalition with the religious parties, nor do they want to sit with Shinui.
One possibility is that Shinui could quit and Labor and the religious parties join the coalition.