The draft, which has not been made public, had a warm preliminary reception from the Israeli and Lebanese governments. But amid domestic opposition in both countries, Lebanon on Tuesday sought amendments from the US envoy.
On Thursday, Israeli Prime Minister Yair Lapid was updated on the details of the substantial changes Lebanon is seeking to make and instructed the negotiating team to reject them, an Israeli official said.
A spokesperson for the US embassy in Jerusalem said the parties were at a critical stage in the negotiations and the gaps have narrowed.
According to Israeli media, a main sticking point was over recognition of a line of demarcation buoys Israel has strung out to sea from its coast. Lebanon worries about any action that may connote formal acceptance of a shared land border.
Lebanon, which has never recognized the state of Israel, with any broader peace deal beyond the horizon - has also said Israel will earn no royalties from the Lebanese share of gas in the Qana prospect.
Top Lebanese negotiator Elias Bou Saab told Reuters on Thursday that he would only respond to official statements and not to media reports on Israel's stance.
He said the deal is 90% done but the remaining 10% could make it or break it, adding that he was in constant contact with US mediator Amos Hochstein.
Israel has been preparing to activate a gas rig, Karish, which is outside Qana. Lebanon's Iran-backed Hezbollah made veiled threats about Karish that lent urgency to the talks.
Israel previously presented the draft deal with Lebanon, if finalized, as securing Karish. But on Thursday, it changed tack.
Israel is now pressing ahead with Karish, regardless of progress or no progress in the talks, whereas before it cast a successful deal as a means of securing Karish.
"Israel will produce gas from the Karish rig as soon as it is possible to do so," the Israeli official said, adding that negotiations will "stop immediately" in the face of any threats.
Defence Minister Benny Gantz further hardened the tone, saying in a speech that "Lebanon will bear a heavy military price" if Hezbollah attacks, and he put forces on alert.
