In a telephone call, Gallant told US Defence Secretary Lloyd Austin that "the possibility for an agreed framework is running out," according to a statement released by his office.

"The trajectory is clear" as long as Hezbollah "continues to tie itself to Hamas," Gallant said, Xinhua news agency reported.

According to the statement, the two also discussed efforts to achieve an agreement for the release of hostages still held by Hamas in Gaza. Gallant emphasised that Israel will "continue to operate with the aim of dismantling Hamas and ensuring the return of hostages held by Hamas in Gaza - by any means."

The call came as White House senior advisor Amos Hochstein arrived in Israel on Monday to discuss the ongoing fighting, in which Israel and Hezbollah have been exchanging fire since October 7 last year, and amid diplomatic efforts to achieve de-escalation between the two.

Hochstein is expected to meet with Israeli Prime Minister Benjamin Netanyahu and Gallant.