Israel has carried out strikes across southern Lebanon, despite a warning from Iran not to continue attacks in the country.

The Lebanese health ministry said eight people were killed in Tyre, where the Israeli military issued a new order for residents to leave the southern city, including its Christian quarter for the first time.

Israel and Iran paused hostilities on Monday, after an Israeli strike on Beirut targeting the Iranian-backed armed group Hezbollah triggered their first exchange of fire since a truce in April.

Iran warned that it could hit Israel again if it did not stop attacks in Lebanon. But Israel vowed to continue its campaign against Hezbollah.

The conflict is complicating President Donald Trump's efforts to strike a deal to end the war between the US, Israel and Iran.

Lebanese media reported that Israeli air and artillery strikes across southern Lebanon killed at least 13 people on Tuesday.

Two people were killed in a pre-dawn drone attack in Kfar Roummane, next to the major town of Nabatieh, according to the state-run National News Agency (NNA).

Later, the Israeli military again told residents of Tyre and its surrounding area to leave their homes immediately and move beyond the Zahrani river, about 30km (20 miles) to the north.

But for the first time, the evacuation order included the Christian quarter, in the city's north-west, where the military alleged that Hezbollah fighters were operating last week.

Roads heading north were busy as residents fled in response to the warning, with mattresses and bags tied to car roofs.

Among them was Elias Barbour, who said he was going to his sister's home in Beirut.

"What have we done wrong? What are we supposed to do?" he told AFP news agency.

Mohammed Mustafa, who was heading to Sidon with his daughter, said he did not want to go.

"It's a lie when they say Hezbollah is here... This is a lie to scare people," he added.

The Israeli military posted its order on social media minutes after reports emerged of air strikes on several buildings in Tyre's eastern al-Massaken al-Shaabiya area.

The Lebanese health ministry said at least eight people were killed and 32 were injured, but added that the figures were provisional because rescuers were still searching through rubble.

In the afternoon, two Syrian nationals were killed in Israeli strikes in the villages of Ansariyeh and Aadloun, which are on the coastal highway north of Tyre, according to NNA.

There was no immediate comment from the Israeli military.

However, the Israeli military's chief of staff, Lt Gen Eyal Zamir, said Israeli forces continued to operate in several areas of southern Lebanon and were dismantling Hezbollah infrastructure.

The Israeli military also said in a separate statement that troops operating in the Ramim Ridge area of northern Israel's Galilee region had shot dead a "terrorist" who crossed into Israeli territory from Lebanon and opened fire towards them.

Hezbollah said on Tuesday that its fighters had launched rockets at a new Israeli military site in the southern border town of Maroun al-Ras, and targeted Israeli troops and military vehicles further north in Qantara and Zawtar al-Sharqiyeh with attack drones.

Lebanon was drawn into the war between Israel, the US and Iran on 2 March, when Hezbollah launched rockets into Israel in retaliation for an Israeli strike that killed Iran's supreme leader.

Israel responded by launching a bombing campaign across Lebanon and invading a significant part of the country's south.

Lebanon's health ministry says at least 3,666 people have been killed there, while Israeli authorities say 30 soldiers and four civilians have been killed on both sides of the border.

Almost one million people in Lebanon - a fifth of the population - remain displaced from their homes and that 1.4 million need humanitarian aid, according to the UN.

The US brokered a ceasefire deal between the Israeli and Lebanese governments on 16 April, but the conflict has continued since then.

The escalation between Israel and Iran began on Sunday.

It followed an Israeli strike in Beirut's southern suburbs - a stronghold of Hezbollah also known as Dahieh - after the group fired two rockets over the border.

Iran fired some 30 ballistic missiles at Israel, while Israel said it carried out two waves of air strikes on Iran. Two Iranian officers were killed, according to Iran's state broadcaster.

On Monday, Iran's armed forces announced that they had stopped operations after delivering a "painful response" to Israel. They also pledged "more severe and crushing measures" if Israel carried out more attacks, including in Lebanon.

Israeli Prime Minister Benjamin Netanyahu said his country was holding fire "at the moment". But he stressed that the struggle against Iran and Hezbollah was "not finished" and warned that Israel would "respond with overwhelming force" to another Iranian attack.

"Iran's attempt to dictate new rules and alter the reality will fail. We will continue to operate and deepen the damage inflicted on the Hezbollah terrorist organisation while defending the communities of northern Israel," Gen Zamir told Israeli military commanders on Tuesday.