His remarks from the border town of Bint Jbeil came as tens of thousands of residents streamed home after a ceasefire between Israel and Hezbollah took effect before dawn, ending more than a year of hostilities and two months of full-scale war.
They also came as the Lebanese army said it had begun reinforcing its presence in the south.
Responding to an AFP question about Hezbollah fighters' withdrawal north of the Litani River in accordance with the truce, Fadlallah said the matter was "linked to Lebanese state measures and strengthening the army presence".
"There is full cooperation on this issue and there will be no problem there," he said.
The truce, which involves implementing a UN Security Council resolution that ended a 2006 war between Israeli and Hezbollah, requires the group to pull back north of the Litani, some 30 kilometres (20 miles) from the border with Israel.
It also requires the dismantling of Hezbollah's military infrastructure in south Lebanon, where analysts have said it likely has an extensive network of tunnels.
Prime Minister Najib Mikati said the army would shore up its presence in the south, while urging Israel to respect the terms of the ceasefire and withdraw.
The Lebanese military said it had "begun reinforcing its presence in the South Litani sector and extending the state's authority in coordination with the United Nations Interim Force in Lebanon (UNIFIL)".
An AFP journalist saw troops and vehicles in two areas of south Lebanon.
'Will not sit idly by'
Fadlallah said Hezbollah had "no visible weapons or bases" in the south, but at the same time, noted the group "is a secret resistance... not a regular army".
"Hezbollah's people are the people of these villages and towns, and most of the dead are from these villages," he said.
"Nobody can make residents leave their villages."
Lebanon says at least 3,823 people have been killed since Hezbollah began cross-border exchanges with Israel over the Gaza war in October 2023, most of them in recent weeks.
But Fadlallah insisted "it's the Israeli enemy who launched this war", from the bombing of Hezbollah communications devices in mid-September to the huge air strikes which killed longtime leader Hassan Nasrallah and other top commanders.
He said Hezbollah had not wanted "a broader war".
"We had set up a support front (for Gaza) in a narrow area," he said, insisting that Israel "has not won the war".
Israel "announced it wanted to destroy Hezbollah, but today Hezbollah has a strong presence in all Lebanon's regions, particularly south of the Litani", he said defiantly.
Hezbollah has prevented Israel "from realising its objectives in Lebanon", he added.
The group is ready to respond if Israel violates the truce, Fadlallah warned, noting the agreement recognises "the right of the two parties to self-defence".
"When our country is attacked, we will not sit idly by."
