The U.S. and Iran are yet to agree a deal over the Strait of Hormuz.
President Donald Trump announced "major combat operations" against Iran on Feb. 28, with massive joint U.S.-Israeli strikes targeting military, government and infrastructure sites.
Delegations from the U.S. and Iran entered negotiations in June aimed at a war-ending deal based on a memorandum of understanding signed by both countries.
The U.S. and Iran have nonetheless continued to exchange strikes, with the strategic Strait of Hormuz the primary flashpoint.
President Donald Trump posted an image of a map on social media Tuesday that labeled the Strait of Hormuz a "new" U.S. territory.
Trump's post -- which was presented without additional comment -- came after he said last week that he would "pretty soon" be "declaring the Hormuz Strait a territory of the United States."
-ABC News' Nicholas Kerr
Iranian parliament speaker Mohammad Bagher Ghalibaf, who led Tehran's negotiating team in peace talks with the U.S., told the Iranian parliament on Tuesday that the Strait of Hormuz will remain closed until the U.S. accepts Tehran's demands.
"The Strait of Hormuz will not open until the blockade is lifted, frozen assets are released, the oil embargo is lifted and threats and military operations on all fronts end, as well as other terms of the memorandum," Ghalibaf said, as quoted by the semi-official Mehr News Agency.
Ghalibaf was referring to the Memorandum of Understanding signed by the combatants in June, which has thus far failed to produce a full peace settlement.
-ABC News' Joe Simonetti
The United Kingdom Maritime Trade Organization (UKMTO) Centre said in an alert on Tuesday that it received a report of a vessel being struck by an "unknown projectile" while transiting the Strait of Hormuz.
"The impact caused damage to the engine room and resulted in a crew casualty. The remaining crew are currently being assisted by the Omani Coast Guard," the alert read.
Stephane Dujarric, the spokesperson for United Nations Secretary-General Antonio Guterres, on Monday reported an "alarming and concerning intensification of violence" in southern Lebanon over the weekend.
The United Nations Interim Force in Lebanon -- UNIFIL -- recorded what Dujarric said were "intense kinetic activities across its area of operations over the weekend," including several Israel Defense Forces airstrikes, helicopter attacks, indirect fire and maritime actions in Lebanese waters.
"Meanwhile, UNIFIL peacekeepers discovered and neutralised several unexploded ordnance. Peacekeepers also continued to encounter restrictions on their freedom of movement and incidents of aggressive behavior," Dujarric said.
-ABC News' Will Gretsky
