AFP- The United States on Thursday sought to extend a shaky ceasefire between Israel and Lebanon as President Donald Trump voiced optimism at China's efforts on Iran.

A ceasefire between Lebanon and Israel - considered to still be in place despite hundreds of deaths in Israeli strikes - ends on Sunday and violence again flared as the two governments met in Washington.

Israel has pounded Lebanon and invaded its south in response to retaliatory fire from Shia movement Hezbollah following Israel's killing of Iran's supreme leader at the start of the war on February 28.

Israeli and Lebanese ambassadors held the first of two days of talks at the State Department, with Israel bringing along military officers.

"We had a full day of productive and positive talks," a senior State Department official said, expecting more to say on Friday.

A Lebanese official told AFP that the country would seek "the consolidation of the ceasefire" and said: "The first thing is to put an end to the death and destruction."

The two sides last met on April 23 at the White House, where Trump announced a three-week ceasefire extension between the countries, which have technically been at war for decades.

Trump at the time made the bold prediction that during the three-week extension he would welcome Israeli Prime Minister Benjamin Netanyahu and Lebanese President Joseph Aoun to Washington for a historic first summit between the countries.

The summit has not happened, with Aoun saying a security deal and an end to Israeli attacks were needed before such a landmark meeting.

Israel has vowed to keep pursuing attacks against Hezbollah. The Israeli military said Thursday it struck more than 65 more Hezbollah sites across Lebanon.

Lebanon's state-run National News Agency reported Israeli airstrikes on the south and east on Thursday, including on areas not mentioned in an earlier Israeli evacuation warning.

Hezbollah said it targeted Israeli troops in northern Israel with a drone. The Israeli military said several Israeli civilians were injured and evacuated for medical treatment.

Hezbollah lawmaker Ali Ammar denounced the talks in Washington, calling them "free concessions" to Israel.

Israeli attacks since March 2 have killed more than 2,800 people in Lebanon, including at least 200 children, according to Lebanese authorities, a toll Hezbollah says includes its fighters.