The U.S. denied an Iranian state television report on a draft interim peace deal that said maritime traffic through the Strait of Hormuz could return to normal within a month of it coming into effect.

“This report from Iranian controlled media is not true and the MOU they ‘released’ is a complete fabrication,” the White House said in a social media post on Wednesday. “Nobody should believe what Iranian state media is putting out.”

Oil had dropped on the Iranian report, with Brent falling almost 4% to below $96 a barrel. It’s declined more than 7% this week as traders become increasingly more optimistic there will be an agreement.

Other key points include the U.S. lifting its naval blockade on Iranian ports, and the American navy leaving waters surrounding Iran.

The draft also says Iran and Oman will have a mechanism in place to oversee shipping in the strait. That’s one of the most contentious issues holding up a deal, with the U.S. saying vessels must be allowed free passage. Oman has not commented in recent weeks on Iran saying the two are in discussions about managing the strait.

Iran and the U.S. are negotiating to extend their ceasefire by around two months, and to reopen the vital Strait of Hormuz. Tehran’s effective closure of the waterway at the start of the war in February has sent oil and natural gas prices soaring and pushed up inflation globally.

Both Iran and the U.S. have said their talks, via mediators such as Pakistan and Qatar, are making progress. Marco Rubio, U.S. President Donald Trump’s secretary of state, said on May 26 it would take a few more days to reach an agreement.

Tensions remain high, and on May 25 the U.S. killed several Iranian soldiers in an attack on ships it said were laying mines near the strait. Iran fired back at American jets and said it downed an unmanned drone.

“Indirect contacts with the Americans are continuing,” Ali Bagheri-Kani, deputy secretary of Iran’s Supreme National Security Council, said on May 27 in Russia, where he is attending a security forum. “Until we have agreed on all issues, we consider that we have agreed on nothing.”

“There is no doubt that the conditions for passage through the Strait of Hormuz and the procedure for doing so will not be the same as before,” said Bagheri-Kani. “A completely different procedure will be introduced. Iran and Oman, as neighboring coastal states, are holding talks to determine a new mechanism for passage through the Strait of Hormuz.”

The warring sides, who agreed to a fragile ceasefire in early April, also need to agree on what portion of Iranian financial assets will be unfrozen and how quickly. On May 26, Iranian state media said Tehran wants $12 billion unfrozen once the so-called memorandum of understanding — as the two sides are describing the interim deal — is agreed.

Iran hawks in the U.S., including Senator Lindsey Graham, are likely to balk at that, and to pressure Trump to revert to bombing the country.

Another potential obstacle is a parallel war in Lebanon between Israel and Tehran-backed Hezbollah militants.

Israel has stepped up attacks in recent days and said its ground forces are moving further into its northern neighbor’s territory.

Israeli forces will go beyond a strip of land roughly 10 kilometers (6.2 miles) into the south of Lebanon, the military said. Israel has increased strikes elsewhere in the Arab country and killed the new head of the military wing of Hamas, another group allied with Tehran, in Gaza on May 26.

Iran insists the ceasefire has to cover “all fronts,” including Lebanon. Israel, which started the wider war when it bombed Iran alongside the U.S., is reluctant to accept any restrictions on its operations in its northern neighbor. It says its actions are necessary to protect its border communities and counter Hezbollah’s rockets and drones.

Hezbollah, classified as a terrorist organization by the U.S., has “crossed all red lines” with a surge of lethal drone attacks, Eli Cohen, a minister in Netanyahu’s security cabinet, told Israel’s Army Radio.