Iranian President Masoud Pezeshkian on Monday said Tehran remained at the negotiating table after halting attacks on Israel following the first exchange of fire since the April truce.

"Diplomacy and defense are the two wings of national power; we have neither left the battlefield nor the negotiating table," Pezeshkian said in a post on X, adding that Tehran "will not retreat in the face of any threat".

A senior Hezbollah official told AFP on Monday that the Iran-backed group has had "no direct contact" with President Donald Trump, despite recent statements from the US leader suggesting otherwise.

Washington considers Hezbollah a "terrorist" group, including both its military and political wings, and recently imposed sanctions on several of its lawmakers.

Israeli bombardment has damaged a World Heritage site in the southern city of Tyre, a culture ministry official told AFP on Monday, as correspondents there saw debris and damage.

One of the oldest cities on the Mediterranean coast, Tyre lies around 20 kilometers from the Israeli border, and its UNESCO World Heritage listed ruins are located in two main areas of the city.

Local media in Iran said Monday that a "hostile drone" was shot down over the capital Tehran during the new round of fighting with Israel.

"A hostile drone belonging to the American-Zionist enemy was targeted and destroyed by air defenses in the skies over Tehran," the Mehr news agency reported, without elaborating.

The Israeli military said Monday it had struck and dismantled Iranian defense systems deployed across several areas in the country.

"Recently, defense systems were deployed in numerous areas across Iran as part of the regime's efforts to restore its detection and defense capabilities, which were degraded during Operation Roaring Lion," the military said.

Iran said Monday that the United States held responsibility for the resumption of fighting with Israel, saying Israel's actions "cannot be separated" from U.S. policy.

"Without a doubt, as I said, the actions of the Zionist regime in the region cannot be separated from U.S. policies," foreign ministry spokesman Esmaeil Baqaei said at a press conference in Tehran attended by AFP.

The Israeli military has vowed to press ahead with its military campaign in Lebanon and said it would step up operations against Hezbollah.

"The (Iranian) regime is attempting to establish a new equation through direct attacks on Israeli territory in response to IDF operations in Dahieh," military spokesman Brigadier General Effie Defrin said Sunday, in a televised statement.

Israel and Iran traded fire on Monday, seriously testing a fragile truce and threatening hopes for a deal to end the Middle East war.

The new attacks, including a strike on an Iranian petrochemical complex, came hours after U.S. President Donald Trump called on Israel to refrain from retaliating against Tehran's missiles.

U.S. President Donald Trump said Sunday he will call Israeli Prime Minister Benjamin Netanyahu to urge him not to retaliate against Iranian missile strikes on Israel, U.S. news outlet Axios reported.

"I am going to call Bibi right now and tell him not to retaliate," Trump was quoted as saying by Axios journalist Barak Ravid in a phone interview, using the Israeli leader's nickname.

Air raid sirens sounded in Israel on Sunday as its military worked to intercept barrages of incoming Iranian missiles for the first time since an April ceasefire took hold in the Middle East war.

The Israeli army reported the attack just hours after Tehran had threatened to retaliate for a new Israeli strike on Beirut's southern suburbs.