This story is based on conversations with six U.S., Israeli and Lebanese sources with direct knowledge of the negotiations.Four days of nonstop negotiations in Washington this week between the Israeli and Lebanese governments were propelled by one clear shared interest: weakening the influence of Hezbollah and Iran in Lebanon, according to U.S., Israeli and Lebanese officials.Why it matters: The framework brokered by the Trump administration is the most significant political agreement between Israel and Lebanon in four decades — but all parties involved know the vision of peace it lays out may never materialize.Mixed with the skepticism is deep concern that the deal could lead to a violent response from Hezbollah that could throw the country back into civil war. The agreement also seems to contradict some of the understandings reached between the U.S. and Iran in Switzerland, and could thus complicate that fragile truce.The backdrop: Iran managed to wrap the situation in Lebanon into its negotiations with the U.S. in recent weeks.That resulted in a memorandum of understanding that calls on the parties to observe a ceasefire in Lebanon and ensure the country's territorial integrity — which is actively undermined by Israel's ongoing occupation of southern Lebanon.During talks in Switzerland last Sunday, the U.S. and Iran agreed to create a new "deconfliction cell," together with Lebanon and the Pakistani and Qatari mediators, to ensure the ceasefire in Lebanon holds.That shocked both Israeli and Lebanese officials, who saw it as bolstering Hezbollah and legitimizing Iran's influence in the country. The news also came as Israeli and Lebanese diplomats were preparing for a crucial round of negotiations in Washington.Behind the scenes: When they met at the State Department on Tuesday, Israeli Ambassador Yechiel Leiter opened the first session with a strongly worded speech calling the new U.S.-Iranian understandings on Lebanon "a train wreck."Leiter asked the U.S. mediators whether the U.S. was actually still interested in weakening Iran's influence in Lebanon, as the Israel-Lebanon talks had been aiming to do.Lebanon's representatives followed up with their own demands for clarification. "The Lebanese were on their heels," a source with direct knowledge said. While the U.S. mediators stressed the goal was to get an Israeli-Lebanese agreement with no outside interference, the first day of the talks was "pretty ugly," a U.S. official conceded.The parties dug in on their positions, particularly on security issues, and it felt to some participants as though the negotiations were actually moving backward.Zoom in: The talks took place on two tracks: a security track between military officers, and a political track between diplomats. Senior Pentagon and State Department officials mediated. The parties worked on three documents: a framework agreement, a security annex, and an agreement on an initial Israeli withdrawal from two "pilot zones," to be replaced by the Lebanese army.On Wednesday, the negotiations picked up steam. U.S. officials began to think an agreement could be signed the next day.But on Thursday, the tables turned again. As the day passed, the parties hardened their positions, and the U.S. couldn't bridge the gaps on all three documents to create a single package. The main dispute was over the terms and locations of the Israeli withdrawals.On Thursday evening, both Israeli Prime Minister Benjamin Netanyahu and Lebanese President Joseph Aoun hit the brakes. Negotiators on both sides asked for more time to consult with their capitals, and the U.S. mediators agreed to extend the talks by a day.The intrigue: Secretary of State Marco Rubio landed back in Washington on Thursday night after a trip to the Persian Gulf.Rubio had been speaking by phone with both Netanyahu and Aoun since Tuesday, holding around eight calls in total with the two leaders. Vice President Vance also spoke to each leader at least once.Rubio emphasized to Netanyahu and Aoun that it was important to President Trump for a deal to be wrapped up by the end of the week.The high-level attention from Washington "made it clear to both sides that there was a clear sense of urgency here," a source with knowledge said.Inside the room: On Friday morning, Rubio joined the talks to try to close the final gaps. Also involved in the final push were U.S. chief negotiator Dan Holler, U.S. Ambassador to Lebanon Michel Issa, CENTCOM Marines commander Lt. Gen. Joseph Clearfield, and Pentagon officials Daniel Zimmerman and Michael Dimino.The U.S. asked Israel for two changes to the text in order to secure the deal, including an Israeli withdrawal from a village in southern Lebanon currently under Israeli occupation and a clear statement that this would mark the beginning of a broader process of redeployment out of Lebanon.Leiter pressed Netanyahu and other senior Israeli officials to agree in a call that became heated when Netanyahu resisted the changes.