Rubio added that the U.S. reaffirmed its intent to improve the capabilities of the Lebanese Armed Forces "to more effectively establish sovereignty throughout Lebanese territory" with more than $30 million in funds under existing U.S. authorities and appropriations.
The conflict between Israel and Hezbollah broke out when the armed group fired at Israel on March 2, days after the U.S. and Israel attacked Iran. The Hezbollah attacks triggered Israeli air and ground attacks that have killed more than 4,000 people in Lebanon and displaced more than a million.
Lebanon's Moawad also called it a "first step" on the road to restoring Lebanese sovereignty.
"Iran is out, Hezbollah is out, and the road to peace between Israel and Lebanon is in," Leiter said.
Israel describes that territory as a "security zone" or "buffer zone" where its troops can thwart Hezbollah attacks on northern Israel.
Lebanese President Joseph Aoun said the agreement should allow Lebanese to return to "fully liberated" land and rebuilt homes with "no partner" in its sovereignty.
In the latest clashes with Hezbollah, Israel has lost at least 32 soldiers and four civilians. Hezbollah hasn’t shared any numbers on its casualties, but Reuters reported on May 4 that several thousand of its fighters have been killed in the conflict.
A State Department official told Reuters on Thursday that Israel had agreed to pull back from some of the territory it has occupied, something Israeli and Lebanese officials denied.
Before the talks resumed this week, Israel and Hezbollah agreed to halt fire even as Israel kept troops in southern Lebanon.
Violence has persisted since the ceasefire, with Israel saying on Friday its troops had struck and killed what the military described as seven Hezbollah members who were operating near the territory it is occupying. Reuters could not confirm this.
"To the degree that the Lebanese army performs in dismantling and disarming Hezbollah, we will proceed with additional pilot zones and the ultimate determination of an internationally recognized, secure, and agreed upon border," Leiter told reporters after the signing.
Hezbollah lawmaker Hassan Fadlallah said Lebanese authorities would not be able to enforce the agreement unless, with U.S. support, "they go to civil war," pro-Iranian broadcaster Al Mayadeen reported.
Hezbollah would confront any measure taken by Lebanese authorities and would hold on to its weapons even more, adding that the group's opposition was "serious" and would not allow authorities to implement their commitments on the ground, Fadlallah said.