Over 100,000 people have fled to collective shelters as Israel continues strikes on Lebanon.
The president has domestic and international political motivations for touting negotiations to end the war. Iran has similar ones to deny discussions.
Iran does not want a momentary pause in the fighting, fearing that Israel and the United States would use that opportunity to beef up their forces before resuming strikes.
The United States is discussing ways to end hostilities with Iran, even as the Pentagon dispatches more troops.
Ships with no ties to Israel or the United States would be allowed to pass, the government said, but it was unclear if any vessels would try.
The 15-point plan was delivered via Pakistan, whose army chief has emerged as the key interlocutor between the United States and Iran, officials say.
Our national security correspondent David E. Sanger looks at President Trump’s trouble handling retaliatory attacks by Iran that have largely choked off the Strait of Hormuz.
The combat forces would come from a brigade of about 3,000 soldiers capable of deploying anywhere in the world within 18 hours.
Israel Katz, the defense minister, said he ordered troops to destroy more bridges and buildings in southern Lebanon, stoking worries that Israel was widening a military-controlled buffer zone there.
Attacks on Saturday injured dozens in Arad and Dimona, two cities closest to Israel’s main nuclear research facility.