Israeli strikes on a town in southern Lebanon killed six people and wounded seven others, state media said Tuesday, as fighting continued despite a ceasefire agreement.

Lebanon's state-run National News Agency (NNA) reported that Israeli strikes Monday night hit a house in Kfardounine, a town about 95 kilometers from capital Beirut.

Israeli Prime Minister Benjamin Netanyahu has said that Israel has destroyed "more than 90%" of Hezbollah's rockets and ballistic missiles, but noted that that "still leaves them with thousands of rockets and some ballistic missiles."

Lebanese leaders urged the U.S. ambassador to Beirut to pressure Israel to halt its attacks as it pounded the country on Monday despite a truce in the Israel-Hezbollah war.

Lebanese authorities on Monday also raised the overall death toll from Israeli strikes since March 2 to 2,869 people.

Prime Minister Nawaf Salam said overnight that his visit to Damascus aimed to elevate the level of cooperation between Lebanon and Syria and strengthen relations based on mutual respect and non-interference in each other's affairs.

He noted that the era of Syrian tutelage over Lebanon and Hezbollah's intervention in Syria had ended.

Israel kept up strikes on south and east Lebanon on Monday despite a ceasefire, targeting Jmayjmeh, al-Qlayleh, Harees, Arnoun, Jarjou', Sojod, Toul, Yohmor Shqif, Kfartebnit, Kfardounine, Shoukine, Ebba, Kfarjoz, Zebdine, Zebqine, Yater, Nabatieh, Safad al-Battikh and Kfar Remman.

Israeli artillery meanwhile shelled the southern towns of Yohmor, Arnoun, Kfartebnit, Nabatieh, Mayfadoun, Majdalzoun, Jebshit, Ali Taher and Qalaway.

The United States will facilitate two days of "intensive talks" between the governments of Israel and Lebanon on May 14 and 15, the U.S. State Department said on Friday

U.S. Secretary of State Marco Rubio blamed Hezbollah Friday for the situation in Lebanon, accusing the group of being fully dependent on Iranian support.

"The reason why Lebanon faces bombings, the reason why Lebanon faces violence, is because of Hezbollah. It is Hezbollah that’s imposing this on them," Rubio told reporters during a visit to Rome.

Commissioner for Equality, Preparedness and Crisis Management, Hadja Lahbib, is in Lebanon this Friday and Saturday to welcome the seventh humanitarian flight landing in Beirut. This Humanitarian Air Bridge will deliver essential health and shelter items – from the EU's own stock and its partners – to the most vulnerable, reaffirming the European Union's solidarity with Lebanon and steadfast humanitarian support to the country.

The Commissioner is meeting with President Joseph Aoun, Prime Minister Nawaf Salam, and Speaker of the Lebanese Parliament Nabih Berri, as well as humanitarian partners on the ground: United Nations agencies, local and international humanitarian actors, and women-led associations. The Commissioner is also visiting EU-funded projects, including shelters, a reception center for Syrian refugees, a children's hospital, a Palestinian refugee camp, and heavily affected areas.

Lebanon and Israel will hold a third round of direct talks in Washington on Thursday and Friday next week.

"Thursday's discussions will focus solely on consolidating the ceasefire, while Friday's discussions will move to other issues related to Israeli withdrawal, the return of captives, the return of displaced persons, and other details," MTV reported.

President Joseph Aoun on Friday told European Commissioner for Equality, Preparedness and Crisis Management, Hadja Lahbib, that "the support provided by the EU to Lebanon must be channeled into exerting pressure to compel Israel to cease fire and refrain from demolishing and bulldozing homes in the villages it occupies in the south, as well as from targeting paramedics, journalists and civil defense personnel."