Iran live updates: Trump posts map labeling Strait of Hormuz 'new' US territory

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

While President Donald Trump said on Monday that the U.S. has "total control" over the Strait of Hormuz, Energy Secretary Chris Wright told Fox News that the Strait is still a "conflict zone" where disruptions to ship traffic remain, acting as hurdles to transporting oil and gas.

Wright said that trackers of the ships going through the Strait have been turned off due to the conflict, meaning public data does not accurately reflect the true number of vessels transiting the Strait. He asserted that 30 ships went through the waterway on Sunday and that "millions" of barrels have been moving through per day.

Wright said that U.S. military escorts of commercial shipping demonstrate the control the U.S. has over traffic in the strait, but did not acknowledge the Iranian threat that necessitates those escorts and that continues to keep traffic low.

Wright was pressed over the fact that these numbers of ships moving through the Strait are still lower than pre-war levels. He said he couldn't predict the future when asked when he thinks those traffic levels would rise.

"We're fixing a 47-year-old problem with this government in Iran and the threat of nuclear weapons, but it does cause some disruption in the short term. President Trump's policies have made us ready for that disruption," Wright said.

When asked about a timeline for the end of the war, Wright said Trump is "playing the long game."

-ABC News' Isabella Murray and Michelle Stoddart