Israel and Lebanon had a "productive and positive" first day of talks in Washington and the discussions will continue on Friday, a senior US State Department official said.
Lebanon is demanding that the ceasefire with Israel be strengthened and extended as the two countries meet for the latest round of talks.
A ceasefire was declared on April 16, but violence has continued despite an initial drop in Israeli air strikes. It is due to expire on Sunday.
“We had a full day of productive and positive talks that lasted from 9am to 5pm," said the US official on Thursday. "We look forward to continuing this tomorrow and hope to have more to share then."
A Lebanese source briefed on the talks told The National that Lebanon's focus is on ensuring the ceasefire is properly respected.
“The key Lebanese demand will be to enforce and consolidate the ceasefire,” the source said.
Despite the truce, Israel has repeatedly struck Hezbollah and the Iran-backed militants have attacked Israeli troops.
At least 380 people have been killed by Israeli attacks, mainly in southern Lebanon, since the ceasefire took effect, according to Lebanon's Health Ministry.
Israel has also issued forced displacement orders to residents of dozens of towns and villages in southern Lebanon.
An Israeli government representative said the talks were taking place with the goal of disarming Hezbollah and reaching a peace agreement.
Israel launched strikes on Lebanon on Wednesday, killing at least 12 people on the eve of talks.
The Israeli army said an explosive drone launched by Hezbollah fell in Israeli territory near the border and injured several civilians.
Hezbollah said it carried out 17 attacks on Israeli troops in the south on Wednesday.
Peace deal this year?
Lebanese President Joseph Aoun's decision to pursue the talks reflects deep divisions in Lebanon over Hezbollah, which has had close ties to Iran's Islamic Revolutionary Guard Corps since the group was founded in 1982. The Lebanese government has sought Hezbollah's disarmament since last year.
A parliamentary source said that in recent days, strong opposition from political forces and figures rejecting the option of direct negotiations with Israel has largely disappeared.
“Whatever objections remain are now being voiced more as a 'principled position' rather than a firm and decisive rejection,” the source said.
A source in the Lebanese presidency said that Beirut had sent representatives to the State Department to repeat its demands for a ceasefire amid repeated Israeli violations.
"The Lebanese position is that if Israel does not comply, then the ceasefire will be the only item on the agenda during the meeting," the source said.
They added that if a ceasefire is secured, Beirut was prepared to discuss a "timeline for a permanent cessation of hostilities, the Israeli withdrawal from Lebanese territory, the start of the Lebanese army’s deployment, scheduling the return of prisoners and correcting the Blue Line after Israeli attempts to establish new boundary lines".
Lebanon is being represented by Nada Hamadeh Moawad, Lebanon’s ambassador to the US, and by special envoy Simon Karam.
Israel is being represented by ambassador Yechiel Leiter and deputy national security adviser Yossi Draznin, while the US delegates include Mike Huckabee, the US ambassador to Israel, Michel Issa, the US ambassador to Lebanon, and adviser Michael Needham.
The Washington talks mark the highest-level contact between Lebanon and Israel in decades.
The meeting on Thursday at the State Department comes after the previous round of talks was hosted by US President Donald Trump at the White House. He said at the time that he saw a “great chance” of Lebanon and Israel making a peace deal this year.
Lebanese Prime Minister Nawaf Salam, in a May 10 interview with the pan-Arab broadcaster Al Arabiya, said Lebanon's principles in negotiations were to shore up the ceasefire, to secure a timetable for Israeli withdrawal and to win the release of Lebanese detainees held by Israel.
The Lebanese Health Ministry says the war has killed 2,896 people in Lebanon since March 2, including 589 women, children and medics. The ministry's toll does not specify how many of the dead were combatants.
About 1.2 million people have been driven from their homes in Lebanon, many of them fleeing from the south.
Israel says 17 of its soldiers have been killed in southern Lebanon, along with two civilians in northern Israel.
