Iran and Oman issued a joint statement on Tuesday affirming their commitment to ensuring safe passage through the Strait of Hormuz, stressing that all arrangements relating to the waterway "must fully respect their sovereignty and sovereign rights."

The two countries agreed to continue discussions through a joint working team between their foreign ministries to reach an understanding on the future management of navigation in the strait and the related charging service "costs," read the statement.

The statement followed talks in Oman's Muscat between Iranian Parliament Speaker Mohammad Bagher Ghalibaf, Iranian Foreign Minister Seyed Abbas Araghchi, and senior Omani officials.

During the talks, Oman reiterated its support for the recently-signed U.S.-Iran peace memorandum of understanding (MoU), and underscored the importance of continued dialogue and coordination to ensure its implementation, read the statement.

Separately, Iran's semi-official Fars news agency reported Tuesday that only a limited number of vessels are allowed to pass through the strait each day based on coordination with the Navy of Iran's Islamic Revolution Guard Corps.

Fars cited an informed military source as saying that the number will vary daily according to conditions.

According to Fars, the strait had been closed in recent days following Israel's "hostile" actions against Lebanon and U.S. "violations" of its commitments under the MoU.

The developments came a day after mediators announced encouraging outcomes from the first round of indirect U.S.-Iran talks in Switzerland, including a 60-day roadmap toward a final agreement and mechanisms to ensure commercial shipping security through the strait and end hostilities in Lebanon.