U.S. Secretary of State Antony Blinken pushed on Wednesday for a halt to fighting in Gaza and a diplomatic solution to conflict in Lebanon, but Israeli strikes on an historic Lebanese port city proved there was no respite yet.

Huge clouds of smoke billowed above residential buildings in Tyre, a UNESCO-listed port city in south Lebanon, which Israel began bombing hours after issuing an order online telling residents to flee central areas.

Tens of thousands of people have already fled Tyre as Israel steps up its campaign to destroy Hezbollah in Lebanon and Hamas in Gaza, both close allies of its arch Middle East enemy Iran.

The port is typically bustling - with fishermen, tourists and even UN peacekeepers on a break from deployments. Israel’s evacuation orders this week have for the first time encompassed swathes of Tyre, right up to its ancient castle.

“We are better off dying with dignity than living on the street,” said Batoum Zalghout, 25, who fled the latest evacuation zone for another part of the city. She said she had been already displaced with her two children five times.

Strikes hit central parts of Tyre for around an hour at midday. The Israeli military said it had targeted Hezbollah command and control centres there, including its southern front headquarters.

There was no immediate comment from Hezbollah. Tyre mayor Hassan Dabouq said the city’s historic sites were not hit.

In northern Israel, rockets fired across the frontier set off air raid sirens and sent people running for shelters. Smoke trails hung over the city of Haifa, which appeared to be from the interception of Hezbollah rockets. One person was badly hurt, according to Israel's ambulance service.

In Gaza, where Israel has intensified an assault on the northern edge of the territory since killing the leader of Hamas last week, health authorities reported at least 20 people killed in fresh Israeli strikes, most in the north.

Among the dead were Mohammed and Bilal Abu Atwi - a driver for UN aid agency UNRWA and his brother - killed in a strike that blasted their UN -marked vehicle in Deir al-Balah.

"Our children have become martyrs as they were serving their community and people," their father Marwan said at the hospital where their bodies were laid out in white plastic bags.

Washington has called on its ally Israel to do more to help Gazans. A failure to address the humanitarian situation in Gaza could create more insurgents, US Defense Secretary Lloyd Austin said. Israel denies blocking aid from the battle zone. Blinken, who has travelled to the Middle East regularly during the war, is making his first trip since Israel killed Hamas leader Yahya Sinwar, its most-wanted enemy, whose death Washington hopes can provide an impetus for peace.

The trip is also the last major US peace push before the November 5 presidential election that could alter US policy.

Washington aims to head off a widening of the conflict in anticipation of Israeli retaliation for an Iranian October 1 missile attack. Blinken said Israel's retaliation should not lead to greater escalation.

After Blinken left Israel, Defence Minister Yoav Gallant visited a military base and told troops that once Israel attacks Iran everyone would understand their strength.

Blinken met with Israeli officials including Prime Minister Benjamin Netanyahu, then travelled to Saudi Arabia and met with Crown Prince Mohammed bin Salman. The State Department said they discussed efforts to end fighting in Gaza and Lebanon.

‘Strategic Success’

In Lebanon, Israel's military said it had killed three Hezbollah commanders and some 70 fighters in the south in the past 48 hours. A day earlier it confirmed it had killed Hashem Safieddine, the militant group's heir apparent leader after Hassan Nasrallah's death in a September 27 Israeli airstrike.

Israeli strikes on Lebanon over the past month have killed nearly the entire leadership of Hezbollah, blows without precedent in the four decades of Israel’s battles against the group. Killing Sinwar last week in Gaza caps that with a major blow to its other big foe, Hamas.

Arriving in Lebanon for talks on how to end hostilities, Germany’s foreign minister Annalena Baerbock said providing arms to Israel posed a dilemma: “On the one hand, Israel is attacked every day and not supporting it would mean that people are not (being) protected ... On the other, it is also Germany's responsibility to stand up for international humanitarian law.”

Blinken said it was now time for Israel to turn its military victories into “an enduring strategic success”, to bring home hostages and to end the conflict with a clear postwar plan.

In the year since fighters directed by Sinwar rampaged through Israeli towns killing 1,200 people and capturing more than 250 hostages, Israel has laid Gaza to waste to root out Hamas, killing nearly 43,000 Palestinians. The past month's strikes on Lebanon have displaced at least 1.2 million Lebanese.

The US sees Sinwar's demise as a chance to bring peace, making it easier for Netanyahu to argue that goals have been achieved in Gaza. But since his death, Israel has intensified an assault on northern areas where it says Hamas has regrouped.

Hospitals have ceased functioning and had run out of coffins. A UN-backed polio vaccination campaign, launched after a Gaza baby was paralysed by the disease, was halted.

“We call on the world, which has failed to provide protection and shelter for our people and has been unable to deliver food and medicine, to make an effort to send shrouds for our fallen,” the Gaza health ministry said in a statement.