There is a rising risk of “full-scale regional war” in the Middle East, the foreign secretary, David Lammy, has warned, amid frantic international efforts to calm tensions with Iran and reach a ceasefire agreement between Israel and Hamas.

With the US secretary of state, Antony Blinken, flying into Israel this weekend to push for a deal, Lammy has joined forces with his French counterpart, Stéphane Séjourné, to warn that now is a “perilous moment” for the region in the midst of widespread fears of escalation involving Tehran and allied militias in Lebanon, Iraq, Syria and Yemen.

In a joint article for the Observer highlighting a growing cooperation between Britain and France, the pair state that the world is witnessing a “destructive cycle of violence” that has to be averted. “Fighting between Israel and Lebanese Hezbollah has intensified,” they write. “Iranian threats of further escalation mean the risks of a full-scale regional war are rising.

“One miscalculation, and the situation risks spiralling into an even deeper and more intractable conflict. This cycle, with its tendency towards escalation, is making progress towards a political solution harder.”

Tensions soared further on Saturday between Israel and the powerful Lebanese militia after an Israeli military airstrike in the south of the country killed at least 10 Syrian nationals. Israel said it had targeted a Hezbollah weapons depot.

The strike in Nabatieh province was one of the deadliest single Israeli attacks on Lebanon since Hezbollah and Israel started trading cross-­border fire the day after the 7 October Hamas invasion that triggered the war in Gaza. Hezbollah and Iran’s other regional allies have said they will stop attacking Israel when the war in Gaza is brought to an end.

The intervention from the two foreign ministers marks the latest sign of Lammy’s increasing willingness to work with European allies and follows the first joint UK-France visit in more than 10 years, when the pair visited Israel and the occupied Palestinian territories last week.

They say their trip shows “a new spirit of cooperation, in the interests of our national security, Europe’s security and the Middle East’s security”.

Their concerns over escalation come amid fears over Iranian retaliation against Israel after the assassination of Hamas’s political leader, Ismail Haniyeh, in Tehran last month, as well as the killing of a top Hezbollah commander in Beirut.

Israel did not claim responsibility for Haniyeh’s death, but the Mossad, its intelligence agency, is well known for carrying out targeted killing operations overseas.

“An all-out conflict across the region is in nobody’s interests,” Lammy and Séjourné write. “All parties need to show restraint and invest in diplomacy. Any Iranian attack would have devastating consequences, not least in undermining current Gaza ceasefire negotiations.

“Our engagement reinforces our conviction that urgently securing such a deal is in the interests of Israelis, Palestinians and the wider region. Only a deal can relieve civilian suffering. Only a deal can restore communities’ sense of security. Only a deal can open up the space for progress towards a two-state solution – the only long-term route to safety, security and dignity for Israelis and Palestinians alike.”

Their comments coincide with Blinken arriving in Israel on Saturday to push for a deal that would secure a ceasefire and sanction the release of hostages from Gaza. The latest round of ceasefire talks in Doha ended on Friday without a breakthrough, but further negotiations are scheduled for this week in Cairo.

However, optimism from international mediators Qatar and Egypt, as well as US president Joe Biden, that talks are progressing well was dismissed by Hamas on Saturday.

Several rounds of negotiations since December have failed. “To say that we are getting close to a deal is an illusion,” Hamas political bureau member Sami Abu Zuhri said to AFP. “We are not facing a deal or real negotiations, but rather the imposing of American diktats.”

Although Hamas and Israel agreed in principle last month to implement a three-phase plan publicly proposed by Biden in May, both sides have since requested “amendments” and “clarifications”, leaving talks at an impasse.

Gaps include the continuing presence of Israeli troops on the Gaza-Egypt border, the sequencing of a hostage release, and the return of civilians from southern to northern Gaza. The Israeli prime minister, Benjamin Netanyahu, has been accused by critics home and abroad of stalling for his own political gain.

The flurry of international activity to secure some kind of de-escalation comes as local health authorities reported that the Palestinian death toll in Gaza had surpassed 40,000 people. The strip has also recorded its first case of polio in 25 years.

An Israeli military airstrike on Az-Zawayda in central Gaza killed another 15 people from a single family, civil defence rescuers in the besieged territory said on Saturday.

About 170,000 displaced people are once again on the move across central and southern Gaza after fresh evacuation orders from Israel’s military, including areas previously designated as humanitarian “safe zones”.

The Israel Defense Forces announced a new ground operation in the Khan Younis area last week after it said areas it had told civilians to flee to had been used by Hamas to fire mortars and rockets towards Israel.

“This is one of the largest evacuation orders affecting the zone to date and it shrinks the size of the so-called ‘humanitarian area’ to about 41 sq km, or 11% of the total area of the Gaza Strip,” according to a report from the Office for the Coordination of Humanitarian Affairs, the UN’s humanitarian agency.