Israel has been turning up the heat on Hezbollah since it began incursions into the region after killing Hezbollah leaders and commanders, including its veteran secretary-general Hassan Nasrallah last month in the biggest blow to the group in decades.
"The solution is a ceasefire, we are not speaking from a position of weakness, if the Israelis do not want that, we will continue," Qassem said in a recorded speech.
"But after the ceasefire, according to an indirect agreement, the settlers would return to the north and other steps will be drawn up."
There was no immediate comment from Israel, which says its operation in Lebanon aims to secure the return of tens of thousands of residents forced to flee their homes in northern Israel because of Hezbollah attacks.
Hezbollah reserves the right to attack anywhere in Israel, its deputy chief Naim Qassem says. (AP PHOTO)
Qassem said Hezbollah reserved the right to attack anywhere in Israel because its enemy has done the same in Lebanon.
He said more Israelis will be displaced and "hundreds of thousands, even more than two million, will be in danger at any time, at any hour, on any day".
"We will focus on targeting the Israeli military and its centres and barracks," he said.
On Monday, Prime Minister Benjamin Netanyahu said Israel would continue to attack Hezbollah "without mercy, everywhere in Lebanon - including Beirut".
Israel has issued military evacuation orders affecting more than a quarter of Lebanon, the United Nations refugee agency said on Tuesday, two weeks after the Israeli military began incursions into south Lebanon to battle Hezbollah.
The figures underscore the heavy price Lebanese are paying as Israel tries to destroy the Iran-backed group's infrastructure in their conflict, which resumed a year ago when it began firing rockets at Israel in support of Hamas at the start of the Gaza war.
In Washington DC, US Secretary of State Antony Blinken and Defense Secretary Lloyd Austin said Israel must take steps in the next month to improve the humanitarian situation in Gaza to avoid legal action involving US military aid, according to news reports and sources.
The United States told the UN Security Council last week that Israel needs to address urgently "catastrophic conditions" among civilians in the Gaza Strip and stop limiting aid deliveries.
The UN refugee agency's Middle East director Rema Jamous Imseis said new Israeli orders to leave 20 villages in southern Lebanon meant more than a quarter of the country was now affected.
"People are heeding these calls to evacuate, and they're fleeing with almost nothing," she told a briefing in Geneva.
Israeli strikes have killed at least 2350 people over the last year, the Lebanese health ministry said, and more than 1.2 million people in Lebanon have been displaced.
The majority have been killed since late September when Israel expanded its military campaign.
The toll does not distinguish between civilians and combatants.
The health ministry said 41 people were killed and 124 were wounded on Monday.
About 50 Israelis, both soldiers and civilians, have been killed, according to Israel.
Israel expanded its bombing campaign in Lebanon on Monday, killing at least 22 people in a strike in the north on a house where displaced people were sheltering, health officials said.
"What we are hearing is that amongst the 22 people killed were 12 women and two children," UN human rights office spokesman Jeremy Laurence said of the strike on Christian-majority Aitou.
He called for an investigation into the strike which he said has raised concerns with respect to "the laws of war".
Rescue workers were still pulling bodies out of the rubble in Aitou on Tuesday, local media reported.
Israel has not commented on the strike but says it takes all possible precautions to avoid civilian casualties.
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