Israel and the US have bombarded Iran and Lebanon with a fresh wave of airstrikes and threatened a major escalation in their joint offensive, as Iran retaliated with more attacks across a swath of the Middle East.

Pete Hegseth, the US defence secretary, said US firepower was “about to surge dramatically” with the deployment of more bombers, while Eyal Zamir, the Israel Defense Forces chief of staff, said Israel was moving to a new phase of its offensive that would “further dismantle the regime and its military capabilities”.

Zamir said in a statement: “We have additional surprises ahead which I do not intend to disclose.”

On Friday, the seventh day of the spiralling conflict, Tehran launched missiles and drones at Kuwait, Qatar, Saudi Arabia, Bahrain, apparently targeting US bases and civilian infrastructure including oil pipelines.

Other missiles were launched at Israel, though fewer than in the first days of the conflict. Iran’s Revolutionary Guards said they had fired missiles towards Tel Aviv after an earlier wave of explosions caused a blaze at a residential building in the city.

The Revolutionary Guards said Iranian forces had also targeted a military airbase and a radar site in Israel, and promised new initiatives and weapons would soon be deployed to confront Israeli and US aggression, without giving details.

Witnesses described the latest airstrikes in Iran as particularly intense, shaking homes in the capital Tehran. Others reported explosions around the Iranian city of Kermanshah in an area that is home to missile bases. Internet coverage in Iran is running at about 1%, according to the monitor group NetBlocks, limiting the availability of information about the impact of the war on ordinary Iranians.

In Lebanon, where the war has triggered renewed fighting between Israel and the Iran-backed Islamist militant movement Hezbollah, many hundreds of thousands were fleeing Israeli strikes in the south of the country, parts of Beirut and the Bekaa valley.

The Israeli army issued a warning on Thursday evening, urging residents of the Dahiyeh, a stronghold of Hezbollah that is also home to more than 600,000 people, to “save your lives and evacuate your homes immediately”.

Hashem Osseiran, a Red Cross spokesperson for the Middle East, described scenes of panic and confusion. “Many people have fled, some on foot, with nothing but the clothes on their backs and no clear sense of where to go,” Osseiran said.

The Lebanese health ministry said the death toll now stood at 123 since the resurgence of hostilities between Israel and Hezbollah, which fired missiles into Israel in the opening days of the war.

The war has killed at least 1,230 people in Iran and about a dozen in Israel, according to officials in those countries. Six US troops have been killed. Oil supplies have been disrupted, tens of thousands of flights have been cancelled, and international stock markets have been roiled.

Iran’s president, Masoud Pezeshkian, said on Friday that “some countries” had begun mediation efforts, without elaborating. Turkey is thought to have made some efforts to bring about a swift end to the conflict but there appears little chance of that happening.

Donald Trump signalled once more that regime change was the objective of the joint US-Israeli offensive, which began with a surprise attack on Saturday that killed Ayatollah Ali Khamenei, Iran’s supreme leader.

In brief remarks at the White House, Trump again urged the Iranian people to “help take back your country”, promising the US would grant them “immunity”.

“So you’ll be perfectly safe with total immunity,” Trump said, without giving any details about what that meant. “Or you’ll face absolutely guaranteed death.”

Analysts have said that defections of senior officers from the army or the Revolutionary Guards would suggest the radical clerical regime’s grip on Iran is weakening. There is no evidence of this so far, however.

Iranian state television reported on Friday that a leadership council had started discussing how to convene the country’s assembly of experts, which will select the new supreme leader.

In Tehran, worshippers gathered for the first Friday prayers since the start of the war. Online footage shared by Iranian media showed crowds of men and women dressed in black, some carrying Iranian flags, streaming to an open space outside the Imam Khomeini Mosalla grand mosque in the capital.

In the background of one video, a man speaking through a loudspeaker mourned Khamenei. “We bear witness that he was the embodiment of piety and guardianship in our time,” he said as some worshippers seated on prayer rugs wept.

In an interview with the news website Axios, Trump said he should be involved in choosing Iran’s new leader and spoke dismissively of Khamenei’s son Mojtaba Khamenei, who is a frontrunner to replace his father, calling him “a lightweight”. “We want someone that will bring harmony and peace to Iran,” Trump said.

Recent waves of Israeli strikes appear to have been focused on Iran’s western border with Iraq, possibly preparing for incursion by fighters from Iranian Kurdish opposition groups based in northern Iraq.

Qatar and Saudi Arabia both said they had intercepted Iranian attacks targeting US bases in each country. In Bahrain, officials said Iranian strikes targeted two hotels and a residential building. In Kuwait, where the six US soldiers were killed on Sunday, the army said air defences were activated when missile and drone attacks breached its airspace.

The British ambassador to Bahrain said on Friday the UK would help defend the country with its fighter jets. It came a day after the UK prime minister, Keir Starmer, said he was sending four more Royal Air Force Typhoon fighters to Qatar following requests from allies for further support.

Volker Türk, the UN high commissioner for human rights, said “the world urgently needs to see steps to contain and extinguish this blaze”, but that “instead we are only seeing more inflammatory, bellicose rhetoric, more bombings, more destruction, killings and escalation, that fuels it further”.