By Maya Gebeily and Steven Scheer

BEIRUT/JERUSALEM, June 2 (Reuters) - Israel kept up strikes on southern Lebanon on Tuesday, pressing its campaign against Hezbollah a day after U.S. President Donald Trump asked Israeli Prime Minister Benjamin Netanyahu not to attack Beirut, averting further escalation in the three-month-old war.

Following Trump's intervention, Lebanon's government said Israel would refrain from carrying out threatened strikes on the Hezbollah-controlled southern suburbs of Beirut, while the group would halt attacks against Israel.

By Jana Choukeir

DUBAI, June 2 (Reuters) - Iran is reviewing a proposed agreement with the United States to halt the war between the two countries, Iran's Mehr news reported on Tuesday, after U.S. President Donald Trump said talks to reach a deal were continuing.

More than three months after the U.S. and Israel launched strikes against Iran, the conflict has hardened into a stalemate while largely indirect talks to negotiate an interim deal have proved inconclusive, leaving the Strait of Hormuz largely shut.

Israel has portrayed the capture of a Crusader-era fortress as a turning point in its offensive against Hezbollah, but the operation has also sparked fears of a new quagmire in south Lebanon.

Israeli authorities praised the symbolism of the capture of Beaufort, perched atop a rocky outcrop, as they announced its capture in an assault documented by military drones.

Almost 44 years to the day earlier, Israeli forces had seized the same commanding position overlooking a valley, later turning it into a key base during their two-decade occupation of southern Lebanon.

CAIRO, June 2 (Reuters) - Israeli fire killed at least three Palestinians in separate incidents across the Gaza Strip on Tuesday, Gaza health officials said.

Medics said at least one person was killed and four were wounded when an Israeli airstrike hit a vehicle east of Deir Al-Balah in the central Gaza Strip. The blast left the vehicle a mangled skeleton.

Another strike earlier in the day killed one person and wounded another in the nearby Zawayda town, they added, while Israeli gunfire killed one man in northwest Khan Younis, south of the enclave.

Israel and Hezbollah exchanged fire on Tuesday while Lebanese and Israeli envoys met in Washington for direct talks, with US Secretary of State Marco Rubio saying the militant group was the only impediment to a peace deal.

The fighting came after US President Donald Trump declared Monday that he had brokered a deal which the Lebanese embassy in Washington said would at first only cover Israeli attacks on Beirut and Hezbollah attacks on Israeli territory, before expanding in scope.

By Elizabeth Pineau

SARCELLES, France, June 2 (Reuters) - When Bassi Konate became mayor of Sarcelles this spring, the independent candidate backed by the hard-left France Unbowed (LFI) party ended three decades of municipal rule by the Socialists, the traditional powerhouse of the French left.

A native of Sarcelles, a poor, multi-cultural town north of Paris, Konate, 38, leveraged his hometown roots and a network of rappers, soccer stars and influencers to mobilise young voters through social media and canvassing.

Farmer Issa al-Moussa walks among his damaged wheat crop in eastern Syria after the nearby Euphrates River flooded in recent days due to heavy rainfall and increased flows from Turkey.

Syrian authorities have said the country was experiencing an "exceptional" rise in water levels along the Euphrates River, which originates in Turkey and flows through the Raqa and Deir Ezzor provinces before reaching neighbouring Iraq.

UN chief Antonio Guterres said Monday that peacekeepers will be needed in Lebanon after the mandate of the current mission expires at year-end -- an option likely to face opposition from the United States and Israel.

Last August, the UN Security Council, under US pressure, decided to end the mandate of the United Nations Interim Force in Lebanon (UNIFIL) on December 31, 2026.

By Luc Cohen

NEW YORK, June 1 (Reuters) - An alleged member of an Iran-backed militia pleaded not guilty on Monday to U.S. criminal charges he was involved in multiple attacks against American interests in Europe, proclaiming in a courtroom outburst, "I am not a criminal."

BEIRUT, June 1 (Reuters) - Lebanon's embassy in Washington said in a statement on Monday that Hezbollah had accepted a U.S. proposal for a mutual cessation of hostilities that would be extended to encompass all Lebanese territory.

The statement, shared by the Lebanese presidency on X, said the arrangement would first see Israel refrain from striking Beirut's southern suburbs in exchange for Iran-backed Hezbollah halting its attacks against Israel, after Israel had threatened to attack the capital's suburbs on Monday.