According to Lebanon's authorities, Hezbollah would no longer fire into Israel under the agreement, while the Israeli military would cease striking south Beirut, long a bastion of the Iran-backed militant group.The developments followed a dramatic escalation in violence that saw Israeli troops stage their deepest incursion into Lebanon in two decades, conducting waves of heavy bombardment and threatening to strike the south Beirut suburbs.As the violence threatened to scupper a ceasefire in the wider Middle East war between the US and Iran, 24-year-old south Beirut resident Hadi told AFP he had hoped for some stability, but "that feeling did not last long".The Israeli military said air defences intercepted two projectiles that crossed from Lebanon into northern Israel, hours after Trump's announcement.According to Lebanon's National News Agency, Israel conducted fresh air strikes on south Lebanon on Tuesday.Lebanon's embassy in Washington had hours earlier said Hezbollah had accepted a US proposal for a "mutual cessation of attacks", though there has been no official confirmation by the militant group.'For ETERNITY!'"Israel's strikes on Beirut's southern suburbs will cease, and in exchange Hezbollah will not attack Israel. And we will work to ensure the ceasefire expands to include all of Lebanon's territory," the Lebanese presidency said in a statement.Israeli Prime Minister Benjamin Netanyahu said he had told Trump "that if Hezbollah does not cease attacking our towns and our citizens, Israel will strike terrorist targets in Beirut".But Trump doubled down on his ceasefire push, posting on Truth Social that "hopefully" Israel and Hezbollah would stop fighting "for ETERNITY!""There will be no Troops going to Beirut, and any Troops that are on their way, have already been turned back," Trump said after what he described as a "very productive" call with Netanyahu.According to Axios, however, Trump called Netanyahu "fucking crazy" and accused him of putting Iran peace talks at risk."Likewise, through highly placed Representatives, I had a very good call with Hezbollah, and they agreed that all shooting will stop -- That Israel will not attack them, and they will not attack Israel," Trump added.Hezbollah drew Lebanon into the Middle East war on March 2 by firing rockets at Israel in retaliation for the killing of Iran's supreme leader, and Tehran has insisted that Lebanon be included in any peace deal with Washington.According to Iran's Tasnim news agency, Tehran was no longer engaging in talks with Washington due to Israel's offensive. Trading blows