The proposal aims to create a conducive environment for a gradual de-escalation and a cessation of all hostilities, the official says.Washington has put forward a proposal to de-escalate hostilities in Lebanon, a United States official has told Al Jazeera, adding that Secretary of State Marco Rubio has held separate talks with Lebanese President Joseph Aoun and Israeli Prime Minister Benjamin Netanyahu.The statement was made after Israel’s military took over the medieval Beaufort Castle just north of the Litani River in southern Lebanon as it conducts its deepest push into the country in decades.Recommended Stories list of 4 itemsend of listThe US official told Al Jazeera on Sunday that under the proposed “roadmap”, Hezbollah would halt all attacks on Israel in exchange for Israel refraining from further escalation in the Lebanese capital, Beirut.The US proposal aims to create a conducive environment for a gradual de-escalation and a complete, comprehensive cessation of all hostilities, the official added.But Israeli Prime Minister Benjamin Netanyahu, who promised to push deeper into Lebanon and called Sunday’s operation a “dramatic shift” in the campaign against Hezbollah, ordered the military on Monday to attack targets in Beirut’s southern suburbs, known as Dahiyeh, a stronghold of the Lebanese group.The US official placed responsibility for the current round of fighting squarely on Hezbollah and accused it of following Iran’s directives without regard for Lebanese interests.Iran, the official added, was prolonging the conflict in Lebanon to position itself as a mediator.“The quickest way to protect civilians and reduce escalation is for Hezbollah to cease fire immediately,” the official said, adding that Washington …