Hezbollah's leader has criticized a framework agreement that Israel and Lebanon have signed to end months of conflict between the Iran-backed group and Israel, raising concerns about its effectiveness.

The agreement signed Friday in Washington links Israel's withdrawal from Lebanon to Hezbollah's disarmament, something the group rejects.

The Israeli military said an officer was killed and a soldier was wounded on Sunday in fighting in southern Lebanon, two days after Israel and Lebanon signed an agreement aimed at ending hostilities.

Hezbollah lawmaker Hassan Fadlallah warned on Sunday of "internal conflict" in Lebanon over the country's agreement with Israel, which the Iran-backed group rejects, predicting that the deal would not be implemented.

Israel's Prime Minister Benjamin Netanyahu has hailed the U.S.-brokered agreement with Lebanon, calling it a historic achievement that dealt a blow to arch-foes Iran and Hezbollah.

Israel's far-right National Security Minister Itamar Ben Gvir denounced the U.S.-brokered agreement with Lebanon, saying the Lebanese government could not be trusted to disarm Hezbollah.

France has said that it is "ready to contribute" to the framework agreement signed by Lebanon and Israel, adding it should pave the way for the full restoration of Lebanese sovereignty.

The Lebanese military has vowed to maintain public order, after Hezbollah supporters staged street protests against the government's signing of an agreement with Israel.

Israel's defense minister said that Israeli forces had been ordered to prepare for an extended stay in the so-called security zone in southern Lebanon, after Israel and Lebanon agreed on a framework to end hostilities.

President Joseph Aoun told his U.S. counterpart Donald Trump on Saturday that the Lebanese state will assume responsibility for implementing a recent agreement reached with Israel, his office said.

Aoun "said the Lebanese state would assume its responsibilities in implementing the framework agreement and expressed hope that the United States would help prevent any violations of the deal and ensure that all commitments are fulfilled, notably by pressuring Israel to withdraw from the areas it occupies in southern Lebanon to facilitate the deployment of the Lebanese Army up to the international border," Aoun's office said in a statement.

Lebanon and Israel, under U.S. sponsorship, signed an agreement on Friday hoping to end hostilities between them, but experts say it does not guarantee Israeli withdrawal from Lebanon and its implementation depends on Hezbollah and its backer Iran.