Smoke billows over southern Lebanon following an Israeli strike as seen from Tyre, Lebanon, on Wednesday. Reuters

Israel's military chief told troops on Wednesday that air strikes in Lebanon would continue in order to destroy Hizbollah infrastructure and to prepare the way for a possible ground operation by Israeli forces.

Even as he spoke, sources said the United States had started a diplomatic push to stop the fighting in both Gaza and Lebanon, and that proposals were being hammered out at the UN General Assembly in New York.

Israel on Wednesday widened its airstrikes in Lebanon and shot down a missile that the Hizbollah movement said it had aimed at the headquarters of the Mossad intelligence agency near Israel's biggest city, Tel Aviv.

"You hear the jets overhead; we have been striking all day," General Herzi Halevi told Israeli troops on the border with Lebanon, according to a statement from the military.

"This is both to prepare the ground for your possible entry and to continue degrading Hizbollah."

World leaders expressed concern that the conflict - running in parallel to Israel's war in Gaza against the Palestinian Hamas movement - was escalating rapidly as the death toll in Lebanon rose and thousands fled their homes.

US Secretary of State Antony Blinken said Washington and its allies were working tirelessly to avoid a full-blown war between Israel and Hizbollah.

Two Lebanese officials, two Western diplomats, a source familiar with Hizbollah's thinking and a source briefed on the talks, all of whom declined to be named, said Washington was leading a new diplomatic push that for the first time covered both conflicts - in Gaza and Lebanon.

Three Israeli sources said the United States and France were working on ceasefire proposals to resolve the escalating fighting in Lebanon, which Hizbollah began in support of Hamas in Gaza, but that so far no significant progress had been made.

"Risk of escalation in the region is acute ... The best answer is diplomacy, and our coordinated efforts are vital to preventing further escalation," Blinken said at a meeting with Gulf Arab state officials and ministers in New York.

Israeli airstrikes this week have targeted Hizbollah leaders and hit hundreds of sites deep inside Lebanon while the group has fired barrages of rockets into Israel, where thousands have fled the border region. Hundreds of Lebanese have been killed.

Reuters