Najib Mikati expressed his hopes for peace after speaking to American envoy Amos Hochstein.
But he was speaking just hours after Israeli air strikes on his country killed at least 19 people and rockets launched from Lebanon left seven more dead in Israel.
Despite the continuing violence, Mr Mikati said a draft deal had been written by the US and dated October 26, which would see Israel pull out within a week of the truce starting.
He said the ceasefire would last for an initial 60 days and the deal would include Israel's "right to act in selfdefence" against imminent threats.
The PM told Lebanon's AI Jadeed TV station that Mr Hochstein had suggested "we could reach an agreement before the end of the month and before November 5" - the date of the American election.
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