Israeli foreign minister’s remarks come a day after its defence minister claimed his country had defeated Hezbollah.

Israel says there has been “certain progress” in talks about a ceasefire in Lebanon, although the Iran-backed Hezbollah group says it has not received any peace proposal yet.

Israeli Foreign Minister Gideon Saar said on Monday the main challenge would be enforcing any ceasefire agreement, and that Israel was working with the United States on the diplomatic efforts.

“We will be ready to be there if we know, first of all, that Hezbollah is not on our border, is north of the Litani River, and that Hezbollah will not be able to arm again with new weapons systems,” he added.

The Litani River runs across southern Lebanon, some 30km (20 miles) north of the Israeli border.

Saar’s comments came a day after newly appointed Defence Minister Israel Katz claimed the Israeli military had defeated Hezbollah, and that eliminating its leader Hassan Nasrallah was the crowning achievement.

“Now it is our job to continue to put pressure in order to bring about the fruits of that victory,” Katz said on Sunday.

In Beirut, a Hezbollah official acknowledged that diplomatic efforts had intensified, adding that neither the group nor the Lebanese government had received any new proposal.

“There is a great movement between Washington and Moscow and Tehran and a number of capitals,” Mohammad Afif said in a televised news conference. “I believe that we are still in the phase of testing the waters and presenting initial ideas and proactive discussions, but so far there is nothing actual yet.”

Yedioth Ahronoth, Israel’s best-selling newspaper, reported on Monday that Israel and Lebanon had exchanged drafts through US envoy Amos Hochstein, signalling progress in efforts to reach an agreement.

Since late September, Israel has sent troops into southern Lebanon with the stated aim of securing its northern border from Hezbollah’s rocket attacks and allowing more than 60,000 displaced civilians to return to their homes in the north.

Israel has also intensified air strikes across Lebanon, hitting the eastern Bekaa region, the southern suburbs of capital Beirut and the country’s south – all the areas where Hezbollah holds sway. It has also inflicted heavy losses on the group’s leadership, killing several of its senior members, including Nasrallah on September 27.

Israel expanded its war to Lebanon with the aim of dismantling Hezbollah’s infrastructure after more than a year of near-daily fire exchanges along the Lebanon-Israel border. The Iran-backed group supports the Palestinian Hamas group based in Gaza.

But the extent of destruction inflicted by the Israeli army – from the mass detonation of thousands of residential buildings in the south to it forcibly displacing tens of thousands of people across hundreds of villages – has raised questions over Israel’s intent, suggesting there is a systematic campaign to clear the area.

While Israel has the upper hand when it comes to fighting Hezbollah, its continuous pummelling of Lebanon indicates a “hidden agenda”, Sultan Barakat, senior professor in public policy at Qatar’s Hamad Bin Khalifa University, told Al Jazeera.

“I think there is a level of coordination going on regionally and potentially nationally. [They are] only after the infrastructure of the Shia community in Lebanon,” he said.

“There is a contradiction between saying we won the war and then wanting to continue in this war unless the hidden agenda is really to increase the pressure on Lebanon … to a level where Lebanon becomes irrelevant in any future deal,” Barakat added.