Israel and the Lebanese militant group Hezbollah may be moving towards an agreement on a cease-fire, despite a new round of fighting that has flared up across the two countries' borders.

The Israeli air force carried out heavy strikes in the suburbs of Beirut early Monday, in response to a barrage of about 250 Hezbollah rockets that pounded targets in northern Israel.

However, Israeli Ambassador to the UN Danny Denon believes a ceasefire deal may soon be reached. He said talks were not yet "finalized" but were "moving forward." Israeli media reported that the country's war cabinet was set to discuss the details as early as Tuesday.

The US, too, has been pushing for a deal. White House National Security Communications Advisor John Kirby also expressed hope, saying the talks were "positive" and headed in the right direction.

According to Reuters, senior Lebanese sources suggested on Monday that US President Joe Biden and French President Emmanuel Macron are expected to announce a ceasefire agreement in Lebanon within 36 hours.

Talks to end the fighting between Israeli forces and Hamas militants in Gaza, however, have stalled.

UN officials say that, with winter approaching, residents of the enclave have an urgent need for warm clothing and beds. They say roughly 2 million people have been displaced, nearly 90 percent of Gaza's population. Many of them were forced to flee from the north, but the danger keeps following them.