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A ceasefire deal between Israel and the Lebanese militant group Hezbollah is “very close,” a regional source told CNN on Sunday, even as an uptick in Israeli attacks saw the death toll in Lebanon since mid-September pass a grim milestone.

More than 3,000 people have been killed in Israeli attacks since the uptick in hostilities in mid-September according to a CNN tally of Lebanese health ministry figures, underscoring the urgency of a ceasefire deal.

The regional source suggested that while the deal was closer than ever, it was not fully formed yet. US and Israeli officials cautioned no green light had been given to mediators yet.

“We are moving in this direction, but there are still some issues to address,” a spokesperson for Israeli Prime Minister Benjamin Netanyahu told CNN.

In recent days Hezbollah has been considering a US-Israeli proposal for a 60-day pause in fighting that some hope could form the basis of a lasting ceasefire.

Israel launched a major offensive in Lebanon in mid-September following months of tit-for-tat border attacks which started when Hezbollah attacked Israel in solidarity with Hamas and Palestinians in Gaza. Since then, Israel has launched a ground invasion, killed a string of Hezbollah leaders – including one of its founders, Hassan Nasrallah – and injured thousands of people in an attack featuring exploding pagers.

US envoy Amos Hochstein has been holding talks this week with regional officials to try to reach a deal. On Sunday, CNN analyst and Axios reporter Barak Ravid cited a source as saying Hochstein had told the Israeli ambassador to Washington on Saturday that if Israel did not respond positively in the coming days to the ceasefire proposal, he would withdraw from the mediation efforts.

Earlier Sunday, an Israeli official told CNN Netanyahu had held a security consultation regarding the ceasefire proposals.