Hezbollah drew Lebanon into the Middle East war on March 2, and Israeli and Lebanese representatives have since met twice in Washington, the first such meetings in decades, for discussions that Hezbollah has categorically rejected.

After the first talks, US President Donald Trump announced a 10-day ceasefire that began on April 17, and a three-week extension after the second round.

Trump said he hoped to host Aoun and Israeli Prime Minister Benjamin Netanyahu "over the next couple of weeks" as the two countries prepare for direct negotiations.

Israel "must first fully implement the ceasefire in order to move on to negotiations... Israeli attacks cannot continue as they are," Aoun said in a statement shared by the presidency.

"We are now waiting for the United States to set a date to begin direct negotiations" with Israel, he added.

Israel has repeatedly bombed Lebanon, particularly the south, despite the truce, and has carried out demolitions of border villages inside a "Yellow Line" it established in southern Lebanon.

It said on Wednesday that it struck "approximately 20 command centres and military structures used by Hezbollah".

Israel's military chief Eyal Zamir vowed to continue attacks on "any threat, anywhere, against our communities or our forces -- including beyond the Yellow Line and north of the Litani", referring to a river located around 30 kilometres (20 miles) north of Israel.

In a military statement shared after his visit to Israeli troops positioned in southern Lebanon, Zamir added they may be "required to remain" in certain positions in the country.

Lebanon's state-run National News Agency (NNA) reported a series of Israeli strikes on the country.

Hezbollah meanwhile claimed responsibility for attacks on Israeli troops in southern Lebanon, and drone and rocket fire on northern Israel, saying it is in response to ceasefire "violations".

- 'Consolidate the ceasefire' -

A Lebanese soldier and his brother were killed in an Israeli strike on Wednesday, Lebanon's military said.

The raid comes one day after 19 people including three civil defence personnel were killed in strikes in the country's south, according to updated health ministry figures, while two army troops were also wounded.

Prime Minister Nawaf Salam called the strike that killed the civil defence workers a "war crime".

Aoun in an earlier statement on Wednesday said that authorities were keeping up "contacts to consolidate the ceasefire and stop the demolition of homes in occupied southern villages", according to a statement from his office.

Under the truce, Israel reserves the right to act against "planned, imminent or ongoing attacks".

Israeli strikes in Lebanon have killed more than 60 people since the ceasefire began less than two weeks ago, according to an AFP tally of health ministry and army statements.

Hezbollah lawmaker Hassan Fadlallah vowed Wednesday that Israeli attempts to "establish a security belt on our land... will be brought down by the sacrifices of the resistance and the steadfastness of our people".

He also reiterated his party's rejection of direct talks with Israel.

Planned direct negotiations with Israel have caused a strong rift between the government and Hezbollah, which previously rejected Beirut's commitment to disarming it.

Aoun on Monday stated that direct negotiations aimed at stopping the war, securing an Israeli withdrawal from the south, returning the displaced to their homes, demarcating the border and reaching an end to the "state of hostility" with Israel.