US President Donald Trump told CBS in a phone interview on Saturday that the two sides were "getting a lot closer" to a deal, but also warned that if they do not reach an agreement "we're going to have a situation where no country will ever be hit as hard as they're about to be hit".

Iran said gaps remain between the parties, and the dispute over its nuclear programme would not be part of the initial talks, but that it was finalising a 14-point framework for a deal.

In a sign of the uncertainty surrounding the outcome of the talks, Trump also told another US outlet, Axios, on Saturday that the chances of a deal were a "solid 50/50".

Iranian foreign ministry spokesman Esmaeil Baqaei noted what he called "a trend towards rapprochement" but said "it does not necessarily mean that we and the United States will reach an agreement on the important issues".

"Our intention was first to draft a memorandum of understanding, a kind of framework agreement composed of 14 clauses," he said on state television.

Baqaei added that he hoped the details of a final agreement could be worked out "within a reasonable timeframe between 30 to 60 days" after the framework is finalised.

- 'There is a chance' -

US Secretary of State Marco Rubio also expressed optimism, as Pakistan's army chief, a key go-between between the United States and Iran, left Tehran after two days of talks with senior Iranian leaders.

"There is a chance that, whether it's later today, tomorrow, in a couple days, we may have something to say," Rubio told reporters on Saturday during a visit to New Delhi, adding that he hoped that he would soon be able to announce "good news".

Iran's chief negotiator Mohammad Bagher Ghalibaf had warned earlier that Washington would face a tough response if it resumes hostilities, after US media reports raised the prospect of new strikes and Iranian officials accused the US side of making "excessive demands".

"Our armed forces have rebuilt themselves during the ceasefire period in such a way that if Trump commits another act of folly and restarts the war, it will certainly be more crushing and bitter for the United States than on the first day of the war," Ghalibaf posted on social media.

He issued the warning after meeting in Tehran with Pakistan's army chief Field Marshal Asim Munir, a leading figure in international efforts to negotiate an end to the war, which broke out after the United States and Israel attacked the Islamic republic on February 28.

Weeks of negotiations, including historic face-to-face talks hosted by Islamabad, have still not produced a permanent resolution or restored full access to the Strait of Hormuz, through which a fifth of the world's oil supply transited before the war.

- 'Neither war nor peace' -

The impasse has left ordinary Iranians in limbo.

"The state of 'neither war nor peace' is far filthier than war itself," 39-year-old Tehran resident Shahrzad told AFP.

"I'm about to start a new job, and I'm scared war might break out again -- that I'll end up leaving the job like before, running off to another city out of fear," she said.

Iran's Foreign Minister Abbas Araghchi said in a call with UN Secretary-General Antonio Guterres that Tehran was engaged despite "repeated betrayals of diplomacy and military aggression against Iran, along with contradictory positions and repeated excessive demands" by Washington.

Araghchi held a bevy of diplomatic calls, speaking with his counterparts from Turkey, Iraq, Qatar, and Oman, Iran's official IRNA news agency said.

On another front in the war, Lebanese state media said Israel struck the country's south on Saturday, as fighting has not stopped despite an April 17 ceasefire.

Lebanon's military said one strike targeted a Lebanese army barracks in the south and wounded a soldier.

Hezbollah drew Lebanon into the war on March 2 with rocket fire at Israel after US-Israeli strikes killed Iran's supreme leader.

Hezbollah said Saturday its chief Naim Qassem had received a message from Araghchi indicating that Iran "will not give up its support" for the Lebanese group.

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