Mohammad Bagher Ghalibaf's remarks came as reports emerged that US President Donald Trump had sent a tougher peace proposal back to Iran, and underlined the rift that the parties still need to close.

Any further tweaks to the draft could further delay an agreement to formally end the Middle East war and reopen the Strait of Hormuz after weeks of fraught negotiations marked by sharp rhetoric and occasional flare-ups of violence.

Iran was already in negotiations with the United States about the fate of its nuclear programme in February, when the US and Israel launched air and missile strikes that wiped out much of the Islamic republic's senior leadership.

And, while Tehran has long insisted that its nuclear programme is for purely civilian ends, the United States and its Western allies have long suspected it aims to develop a weapon.

- Nuclear guarantees -

The New York Times and Axios reported on Saturday that Trump had sent back a "tougher" new framework to be considered by Iran, though details remain unclear.

Trump has said his priorities include stopping Iran from any nuclear weapon development and re-opening the Hormuz shipping lane, over which Iran has sought to impose control since the war began.

"The one guarantee that I have to have is that there will be no nuclear weapons. They've agreed to that, and it was very interesting," he told his daughter-in-law Lara Trump in an interview on her Fox News show.

But Tehran has previously cast doubt on Trump's assertions and the sides remain far apart on key issues.

"We will not approve any agreement until we are certain that the rights of the Iranian people have been upheld," Ghalibaf said, in a video broadcast on state television.

According to the Tasnim news agency, "exchanges between Iran and the United States regarding the text of a possible memorandum of understanding are ongoing, with both parties regularly proposing amendments.

"No agreement has yet been finalised, and it is possible that any agreement will be rejected," it said.

Iran has said it needs the release of $12 billion in frozen assets before engaging in substantive talks on its nuclear program, dismissing earlier Trump comments that its enriched uranium stockpile would be destroyed as "baseless", according to Iranian media.

Tehran has also insisted that Lebanon be included in any deal, despite ongoing fighting, with Beirut accusing Israel of a "scorched-earth policy" as it expands operations against Iran-backed Hezbollah.

- Flare-ups -

Though daily strikes throughout Iran and the Gulf halted after Tehran and Washington struck a temporary ceasefire in April and talks mediated by Pakistan, sporadic fighting has continued.

Iran's Revolutionary Guards had shot down a US military drone "about to enter Iranian territorial waters", Iran's state broadcaster IRIB reported, though Washington has not confirmed the incident.

Earlier this week, the worst fighting since the ceasefire erupted when US forces struck the Iranian port of Bandar Abbas, prompting retaliatory fire from Iran.

Nevertheless diplomacy has continued with Trump under pressure to secure a deal that would lift competing US and Iranian blockades around the Strait of Hormuz that have strangled a vital route for global oil supplies.

After Trump said Iran would charge "no tolls" on ships passing through the strait under any deal, Iranian news agency Fars cited sources saying "no such clause" existed.

Iran's ISNA news agency on Saturday quoted lawmaker Alireza Salimi as saying a plan "to implement Iran's management and sovereignty" over the strait -- which includes imposing "administrative fees" for navigation -- would soon go before parliament.

- Lebanon front -

Israeli said Sunday that troops had also crossed the Litani river and raised the Israeli flag over the strategic medieval fortress of Beaufort in southern Lebanon.

Smoke billowed from the surrounding area as the invading army's banner was seen by AFP above the castle, which Israel famously used as a base during their previous two-decade-long occupation.

The push to Beaufort came as the Israeli military issued a sweeping evacuation order to areas south of the Zahrani River, north of the Litani and around 40 kilometres (25 miles) from the border, warning that it was targeting Hezbollah.

"The capture of Beaufort is a dramatic stage and a dramatic shift in the policy we are leading. We have broken the barrier of fear. We are taking the initiative, we are operating on all fronts -- in Syria, in Gaza, in Lebanon," Israeli Prime Minister Benjamin Netanyahu said.

The Israeli military said Sunday that one soldier was killed the previous day in a Hezbollah drone strike.Lebanese Prime Minister Nawaf Salam has accused Israel of pursuing a "scorched-earth policy and collective punishment", and called for "a swift and real ceasefire."

Israel confirmed it was expanding its ground offensive in a statement released early on Sunday, saying "a significant number" of its forces were operating against Hezbollah beyond the Litani river.

A truce between Israel and Hezbollah formally began on April 17 but it has never been observed, with both sides accusing each other of violating it.

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