Israel warned Tuesday that its US ally would not restrain it from striking Hezbollah's bastions in Beirut's suburbs if the Iran-backed group continues to target northern Israeli towns.US President Donald Trump had announced an agreement to halt attacks, but neither side has publicly accepted it and Israel's defence minister said the Lebanese capital's southern suburbs remain potential targets.The warning came hours after Israel's air defences intercepted two projectiles that crossed from Lebanon. According to Lebanon's National News Agency, Israel also conducted fresh air strikes on south Lebanon on Tuesday.Recent days have seen a dramatic escalation in fighting and bombardment as Israeli troops stage their deepest incursion into Lebanon in two decades."If Israeli towns continue to be attacked, we will evacuate and strike the Shiite Dahiyeh quarter in Beirut, Hezbollah's stronghold," Defence Minister Israel Katz told a conference. "The United States endorsed this principle and conveyed it to the Lebanese government and all relevant actors."According to Lebanese authorities, Hezbollah would no longer fire into Israel under the agreement revealed by Trump, while the Israeli military would spare Beirut's southern suburbs, a group of Shia-majority districts where the militants have long held sway.An adviser to Lebanese parliament speaker Nabih Berri, a Hezbollah ally, told AFP that he would guarantee that Hezbollah would respect a "global ceasefire", if one was agreed.The aide, Ali Hamdan, said a "global ceasefire means a halt to Israeli strikes by air, land or sea, and that it will not carry out detonations or demolitions" in the south, where Israel is accused of razing entire villages.- 'For ETERNITY!' -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.As the violence threatened to scupper a ceasefire in the wider Middle East war between the US and Iran, Leila Shahab, 35, a resident of Beirut's southern suburbs, told AFP that she and her family had fled the area after the Israeli threats "because of the kids"."But now we've come back. We found the situation has calmed down a bit," she said."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, echoing Trump."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, later adding in a social media post that he hoped Israel and Hezbollah would stop fighting "for ETERNITY!"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 said.According to Iran's Tasnim news agency, Tehran is no longer engaging in talks with Washington due to Israel's offensive. - Trading blows -