ALSO SEE: Trump Rejects Iran’s Seven-Day Peace Deal to Reopen Strait of Hormuz

Iran insisted on Sunday that only diplomacy can solve its conflict with the United States and Israel after US President Donald Trump said he rejected an Iranian proposal to reopen the Strait of Hormuz and end fighting.

"Our conditions are ‌clear, and any move toward reopening the Strait of Hormuz is contingent on these conditions being met," Iranian Foreign Minister Abbas Araqchi posted on social media. "Only a negotiated solution can get them out of this deadlock."

Iran announced a peace proposal last week at the UN General Assembly in New York, saying it had been transmitted to the Americans via Qatari mediators. Trump said on Saturday he rejected the plan and argued that desperation was driving the Iranians’ push for an agreement on the key waterway.

"They want to make a deal to open the Hormuz Strait immediately because they're losing so badly," Trump told reporters at the White House.

Despite Trump's public statements, mediators facilitating Tehran's talks with Washington have not officially relayed a US rejection of the plan, Araqchi said.

"We are waiting for the mediators to convey the definitive views to us, and we will make a decision based on them," Araqchi posted.

The US ⁠has imposed an economic blockade on Iran to put pressure on Tehran to stop Iranian attacks on vessels in the Strait of Hormuz, which have drastically reduced shipping through the area even as Trump repeatedly asserts that the US controls the waterway.

The commander-in-chief of Iran's army, Amir Hatam, said the war was at a critical and decisive stage, adding that Tehran would not accept a situation in which it was unable to trade while foreign powers used the region's strategic waterways.

"If Iran cannot trade, if Iran cannot live, no one will be able to trade or live," he said, in comments reported by state media.

SAUDI ARABIA DRAWN DEEPER INTO WAR

Previous attempts at diplomacy have failed to end the war, which began on February 28 with US and Israeli strikes on Iran.

Since then it has alternated between pauses and renewed strikes, killing thousands while degrading the conventional forces of Iran and damaging its already ailing economy.

Iran and its allies have responded by extending the conflict throughout the region. Iran has struck US allies in the Gulf with drones and missiles while its Houthi allies in Yemen have hit Saudi interests.

Saudi Arabia, the largest of the Gulf states, has been drawn deeper into the war this month as Houthi fighters have advanced in Yemen, routing forces of the Saudi-backed government and threatening Saudi oil exports through the Red Sea.

The Iran-backed Houthis have repeatedly fired into Saudi Arabia and, in a possible sign of further escalation, ‌parents in Riyadh ⁠received notices from schools on Sunday saying classes would shift to remote learning for the week, according to people who received the messages.

The notice did not give a reason for the decision. Saudi authorities did not immediately respond to a request for comment.

Yemen's Houthi-run health ministry, meanwhile, said seven people were killed and 40 wounded, including children, in a strike on shops at a market at the Mawiya junction in Taiz province, in the southwest.

Later, Yemen's internationally recognised government said its forces had targeted a Houthi military camp and vehicles at the same junction.

CONFLICT HAS DISRUPTED OIL FLOWS, HARMED GLOBAL ECONOMY

The Iranians also engaged their Saudi rivals regarding the Strait of Hormuz during the brief flurry of diplomacy in New York, underscoring the stakes of a seven-month-old conflict that has disrupted oil flows through ⁠a critical shipping lane and taken a toll on the global economy.

Araqchi told reporters at the UN on Friday the proposed deal would trigger a seven-day countdown to reopening the strait and a pause in regional fighting.

"If there is seriousness on the US side to come to a deal and reopen the Strait of Hormuz, everything is now prepared," Araqchi said. If the US were to agree, the warring parties could start wider talks "on mutually agreed subjects."

That could potentially include discussions of Iran's nuclear programme. Trump has cited preventing Tehran ⁠from ever acquiring a nuclear bomb as a key goal, along with ending its ability to attack its neighbours and creating conditions for Iranians to topple their leadership.

US envoy to the United Nations Mike Waltz said on Sunday in an interview with CNN's State of the Union that Trump had rejected the Iranian proposal because it required immediate lifting of sanctions and release of frozen assets.

"So the bottom line is they were asking for everything up front with a promise that they ⁠would then talk," Waltz said. "The president's just not confident that the Iranians are coming in good faith and that they will truly negotiate the end of their nuclear programme."

Iranian President Masoud Pezeshkian, in an interview with the CBS show "Face the Nation", said Tehran was ready for talks on its nuclear programme and other issues, but would not accept "bullying or coercion".

"Iran is not seeking war, but will defend itself against pressure, threats and attacks,” Pezeshkian said, adding that it had already agreed that "we're not supposed to develop nuclear weapons".