WASHINGTON - The negotiation over a deal on ceasefire between Israel and Hezbollah in Lebanon "is going in a very positive direction," a spokesperson for the US National Security Council (NSC) said Monday, stopping short of providing details.

NSC Coordinator for Strategic Communications John Kirby told reporters during a news-of-the-day gaggle that with active involvement by the US government, discussions toward securing the Israel-Hezbollah ceasefire that will lead to both Israeli and Lebanese nationals returning home along the border "were constructive, and we believe that the trajectory of this is going in a very positive direction."

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"Nothing is done until everything is done. Nothing's negotiated till everything is negotiated," Kirby said, adding that "we need to keep at the work to see it through, so that we can actually get the ceasefire for which we've been working for so long and so hard."

If reached, the ceasefire deal will hopefully halt the conflict between Israel and Hezbollah since Israel began a ground incursion into Lebanon in October.

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CNN quoted a spokesperson for Israeli Prime Minister Benjamin Netanyahu as saying Monday that the Israeli cabinet will vote on a ceasefire deal on Tuesday, and that the deal is expected to pass.

Amos Hochstein, the US envoy tasked with mediating the Israel-Hezbollah conflict, said last week in Beirut that a ceasefire was "within our grasp," according to CNN.

Hochstein added a caveat by saying that it was ultimately "the decision of the parties" whether or not a deal may be agreed upon.

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Faced with repetitive requests for disclosing some of the deal's specific contents, ranging from the duration of the ceasefire to a reported clause of US supervision to guarantee no violation by both sides, Kirby simply rejected to reveal any of them, other than saying that the "conversations that Amos had in the region were constructive."

"For me, all that gets into the parameters of the deal itself," Kirby said in reference to the press reporting mentioned by participating journalists at the gaggle.

"I'm just not going to go there."