According to four sources familiar with the matter, the agreement would extend the truce for another 60 days and allow traffic to flow through the strategic waterway while negotiators tackle difficult issues such as Iran's nuclear program.
If approved by leadership in Washington and Tehran, it would amount to the biggest step towards peace since the conflict began on February 28.
News of the possible agreement came after a round of tit-for-tat attacks between the two countries, the latest such incident since the ceasefire took effect in early April. Iran has yet to comment on news of the proposed deal, which was first reported by Axios.
