US Secretary of State Marco Rubio said Washington and Tehran had made progress in talks on the Strait of Hormuz but had not reached a final agreement.
Speaking to journalists at the State Department on August 4, Rubio said he expected an understanding could be reached soon.
He said Oman was mediating discussions aimed at allowing a greater number of commercial vessels to travel through the waterway safely.
Rubio said some commercial ships were already transiting the strait.
He also said oil was continuing to move through Hormuz and that the strait was not completely closed.
US Treasury Secretary Scott Bessent separately said negotiations with Iran were continuing and suggested an understanding could come by Tuesday or Wednesday.
Rubio also referred to security concerns around the Bab el-Mandeb Strait after threats by Yemen's Houthi group against ships linked to Saudi ports.
Bab el-Mandeb lies between Yemen and the Horn of Africa, linking the Gulf of Aden and the Red Sea on a route used by ships travelling through the Suez Canal.
Rubio said that while a Hormuz arrangement was the immediate focus, the United States sought a long-term and final agreement to end Iran's nuclear programme.
No final agreement, terms of a potential deal, or response from Iranian authorities was included in the supplied material.