Hochstein arrived in Beirut on Tuesday, seeking to clinch a ceasefire agreement after the Lebanese government and Hezbollah agreed to a US ceasefire proposal, although with some comments.
"The meeting today built on the meeting yesterday and made additional progress," Hochstein said after his second meeting with parliament Speaker Nabih Berri, endorsed by Hezbollah to negotiate.
"So I will travel from here in a couple hours to Israel to try to bring this to a close if we can," Hochstein said.
US envoy Amos Hochstein hopes talks in Israel can seal a deal on ending the conflict with Hezbollah. (AP PHOTO)
Hezbollah leader Sheikh Naim Qassem said the group had given its own feedback on the truce draft and that it was shared with Hochstein.
He said whether a ceasefire was reached now depended on Israel and whether Prime Minister Benjamin Netanyahu was serious about one.
Hezbollah stood ready to keep on fighting for a long time, he added.
The diplomacy aims to end a conflict that has inflicted massive devastation in Lebanon since Israel went on the offensive against Hezbollah in September, mounting air strikes across wide parts of the country and sending in troops.
Israel says its aim is to secure the return home of tens of thousands of people who fled from its north due to rocket attacks by Hezbollah, which opened fire in support of Hamas at the start of the Gaza Strip war in October 2023.
Hezbollah, still reeling from the killing of its leader Hassan Nasrallah and other commanders, has kept up rocket fire into Israel, targeting Tel Aviv this week, and its fighters are battling Israeli troops on the ground in the south.
Although diplomacy to end the Gaza war has largely stalled, the administration of US President Joe Biden aims to seal a ceasefire in the parallel conflict in Lebanon before president-elect Donald Trump takes office in January.
"We are going to work with the incoming administration. We're already going to be discussing this with them. They will be fully aware of what we're doing," Hochstein said.
Diplomats aim to restore a ceasefire based on a United Nations resolution that ended an earlier conflict in 2006.
Israel has said it wants the freedom to act against Hezbollah if it deems it necessary, even after any truce is agreed.
Lebanon rejects this.
"The condition for any diplomatic settlement in Lebanon is preserving our intelligence capabilities and the (Israeli military's) right to act and protect Israel's citizens from Hezbollah," Israeli Defence Minister Israel Katz told intelligence officers at a meeting on Wednesday.
Hezbollah MP Hassan Fadlallah, in an interview with Lebanese broadcaster al-Jadeed, said he did not want to announce expectations about the chances of a deal being sealed.
Hezbollah was working to "make the political track succeed on national foundations," he added.
Berri has said language about Israeli freedom to act was not included in the draft US proposal submitted to him last week.
UN Security Council resolution 1701 requires the Lebanese state to have a monopoly on arms in the area between border and the Litani River, 30km north of it.
This means Hezbollah should have no military presence near the frontier.
Israel has long complained the resolution was not implemented and Hezbollah remained armed at the border.
Lebanon also accused Israel of regularly violating the resolution.
The casualty toll since October 2023 stands at 3544 people killed in Lebanon, including 902 women and children, the Lebanese health ministry says, the majority of them killed during the Israeli offensive since September.
The figures do not distinguish between combatants and civilians.
Hezbollah strikes have killed 43 civilians in northern Israel and the Israeli-occupied Golan Heights, while 73 soldiers have been killed in strikes in northern Israel and the Golan Heights and in combat in southern Lebanon, according to Israel.
