Israel's Cabinet has proposed a maritime boundary with Lebanon significantly different from the line that Beirut is seeking.
The two countries are racing to stake their own claims for a demarcation line in the Mediterranean Sea, where energy reserves have been found.
They have asked the United Nations to mediate in the matter since Israel and Lebanon have no relations.
The sea boundary dispute could trigger a new conflict over lucrative gas and oil reserves.
Israel recently discovered two gas fields off its coast, and energy companies believe other reserves could be in the area.
Israeli Prime Minister Benjamin Netanyahu says Lebanon's proposed line falls "significantly south" of the line Israeli ministers agreed on Sunday.