U.S. Secretary of State Antony Blinken pushed on Wednesday for a halt to fighting between Israel and militant groups Hamas and Hezbollah, but heavy Israeli airstrikes on a large historic Lebanese port city demonstrated that there was no respite.

Israel began to bomb the UNESCO-listed port city of Tyre on Wednesday roughly three hours after issuing an order online for residents to flee central areas. Huge clouds of thick smoke billowed above residential buildings.

Tens of thousands of people had already fled Tyre in recent weeks as Israel steps up its campaign to destroy Hezbollah in Lebanon and Hamas in Gaza, both close allies of Iran.

The port is typically a bustling hub for the south — with fishermen, tourists and even UN peacekeepers on a break from deployments near the border spending time there by the sea. But Israel's evacuation orders for the city this week have for the first time encompassed swaths of it, including right up to its ancient castle.

Blinken, who has travelled to the Middle East regularly since the outbreak of the war, is making his first trip since Israel killed Hamas leader Yahya Sinwar last week, which Washington hopes can provide a new impetus for peace talks.

The trip is the last major U.S. peace push before a Nov. 5 presidential election between Vice-President Kamala Harris and former president Donald Trump, which could upend U.S. policy in the region.

Washington is also seeking to head off a further widening of the conflict in anticipation of Israeli retaliation for an Iranian Oct. 1 missile attack, launched by Tehran in solidarity with Hezbollah and Hamas. Blinken said on Wednesday that Israel's retaliation should not lead to greater escalation.

Dozens of Hezbollah fighters reported killed 

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 after confirming it had killed Hashem Safieddine, the militant group's heir apparent leader.

Blinken, who held talks with Prime Minister Benjamin Netanyahu on his first stop, said it was time for Israel to capitalize on its military victories.

"Now is the time to turn those successes into an enduring strategic success," he told reporters as he prepared to leave for Saudi Arabia on the next stage of his regional tour. "The focus needs to be on getting the hostages home, ending this war and having a clear plan for what follows."

Blinken's visit to Jordan, planned for Wednesday, was postponed, Jordan's foreign minister said, without giving a reason or rescheduled date.

WATCH | Blinken aims to revive efforts to secure Gaza ceasefire, as Israel bombs Beirut: 

Blinken ramps up Israel-Hamas ceasefire efforts as northern Gaza, Beirut under fire

U.S. Secretary of State Antony Blinken met Tuesday with Netanyahu as part of his 11th visit to the region since the outbreak of the Israel-Hamas war. After Israel's killing last week of Hamas leader Yahya Sinwar, Blinken is trying to revive efforts to secure a ceasefire in Gaza. Israeli military forces besieged hospitals and shelters for displaced people in the northern Gaza Strip on Monday. The Israeli military levelled a building in a suburb of Beirut on Tuesday.

Hamas leader Sinwar, whom Israel killed last week, was the suspected mastermind of the Oct. 7, 2023 attack on Israel, when Hamas-led militants killed some 1,200 people and abducting another 250, by Israeli tallies. Israel's offensive in Gaza has killed over 42,000 Palestinians, according to the enclave's health authority.

Over the past month, Israel has also dramatically ramped up its war in Lebanon against Hezbollah, another Iran-backed militant group that had rocketed Israel in support of the Palestinians. Israel has launched a ground offensive and killed most of Hezbollah's leadership in airstrikes that have displaced 1.2 million people.

Both sides in Gaza war holding firm

Washington views Sinwar's death as a chance to push for peace, as it would now be easier for Netanyahu to argue that major goals have been achieved in Gaza.

Blinken said new formulations were being examined in an effort to win freedom for Israeli hostages held in Gaza and bring an end to the war.

Still, there has been no sign of a let-up in fighting. Hamas says it will not free scores of hostages it is still holding without an Israeli promise to end the war in Gaza. Israel says it will not stop fighting in Gaza until Hamas is annihilated, and in Lebanon until Hezbollah no longer poses a threat.

Diplomats say Israel is pressing its military advantage to lock in a strong position before a new U.S. administration takes office following the Nov. 5 election.

Israel's military said its forces in southern Lebanon were continuing to conduct "limited, localized, targeted raids against Hezbollah terrorist infrastructure and operatives."

"Over the past day, the troops eliminated approximately 70 terrorists in ground and aerial strikes," it said.

Israel's offensive has driven at least 1.2 million Lebanese from their homes and killed 2,530 people, including at least 63 over the past 24 hours, the Lebanese government said on Tuesday.

On Tuesday, the military said it had confirmed the killing of Safieddine, heir apparent to Hezbollah leader Hassan Nasrallah who was killed in an Israeli attack last month. The military said Safieddine was killed in a strike three weeks ago in Beirut's southern suburbs; Israel had earlier said he had probably been killed, but had stopped short of confirming so.

There was no immediate response from Hezbollah, which Nasrallah had turned into a powerful military and political force, but now faces its most serious setbacks since it was formed by Iran's Revolutionary Guards in 1982 to counter an Israeli invasion of Lebanon.