Hello and welcome to the Guardian’s continuing coverage of the crisis in the Middle East.

Donald Trump has hailed an agreement to de-escalate the fighting in Lebanon, which has killed thousands of people and inflamed tensions in the broader US-Israeli war with Iran.

Trump said Hezbollah, through intermediaries, had pledged not to attack Israel, while Israeli prime minister Benjamin Netanyahu agreed to pull back any troops preparing to attack Beirut.

“Let’s see how long that lasts – Hopefully it will be for ETERNITY!” Trump wrote on his Truth Social platform.

According to Lebanon’s embassy in Washington, the agreement would not end the conflict in that country. But it calls for Israel to refrain from strikes on Beirut and its suburbs controlled by Hezbollah, while the Iran-aligned group would halt its attacks on Israel.

Despite the agreement, hostilities in southern Lebanon – which Israel invaded in March – appeared to continue. This morning, the Israeli military said that it intercepted two projectiles that crossed from Lebanon into northern Israel, and that no injuries were reported.

After Trump’s announcement, Netanyahu said Israel would continue military operations in southern Lebanon, where ground forces are pushing toward the Zahrani River, their deepest incursion in Lebanon in 25 years. His statement made no mention of a new ceasefire.

Hezbollah lawmaker Hassan Fadlallah said the group would support a full ceasefire across all Lebanon as a precursor to the withdrawal of Israeli troops. He did not say whether the group would stop its strikes on Israeli territory.

Lebanon said it would seek to expand the ceasefire in talks with Israel in Washington tomorrow. That could clear the path for renewed efforts to end the three-month-old war that began with US and Israeli attacks on Iran. The process has been stuck in limbo for weeks under a fragile ceasefire as negotiators have been unable to agree on an initial framework for peace talks.

In other developments:

• Iran’s Revolutionary Guards (IRGC) threatened to open “new fronts” and keep the strait of Hormuz closed over Israel’s offensive in Lebanon, state media reported. “Iran considers crossing the red lines in Lebanon and Gaza to mean direct war,” state TV quoted the IRGC’ intelligence organisation as saying.

• The ceasefire already in place between Iran and the US is unequivocally a ceasefire on all fronts, including in Lebanon, Iran’s top diplomat said yesterday after Netanyahu ordered attacks on the Hezbollah-controlled southern suburbs of Beirut. “Violation on one front is a violation of the ceasefire on all fronts. The US and Israel are responsible for the consequences of any violation,” foreign minister Abbas Araghchi wrote on X.

• US secretary of state Marco Rubio will face questions at Congress today for the first time since the Iran war began. He will testify before House and Senate committees on the state department’s 2027 budget request, where he is expected to face questions about Trump’s war efforts and shifting diplomatic goals.

• Oil prices jumped and equities slid as Middle East peace talks stumbled and tensions mounted between Iran and the US. Crude futures shot more than 5% higher yesterday as an Iranian news agency announced Tehran had suspended the negotiations with the US via mediators, AFP reported.

• US forces intercepted two Iranian ballistic missiles targeting American forces based in Kuwait late on Sunday, the US military said yesterday. No American personnel were harmed, it added.