The Israeli military has warned residents in 24 areas in Lebanon – including 14 in the capital Beirut – that it plans to carry out strikes in the coming hours and throughout the night.
The Israel Defense Forces (IDF) said it would target banks and other financial infrastructure supporting Hezbollah.
A BBC correspondent in Beirut said there have been eight air strikes in the capital’s southern Dahieh district, an area controlled by Hezbollah.
Lebanon’s state-run media also reported a strike in the east of the country. It is unclear whether there were any casualties.
Meanwhile, Hezbollah said it had fired more rockets into Israel on Sunday, targeting military bases.
In a statement on Sunday evening, IDF spokesman Rear Adm Daniel Hagari warned that “anyone located near sites used to fund Hezbollah’s terror activities must move away from these locations immediately”.
“We will strike several targets in the coming hours and additional targets throughout the night,” he said.
“In the coming days, we will reveal how Iran funds Hezbollah’s terror activities by using civilian institutions, associations, and NGOs that act as fronts for terrorism,” the Israeli spokesman added.
Lebanon’s state-run National News Agency (NNA) reported a strike on the bank Al-Qard Al-Hassan association in the country’s eastern Bekaa Valley.
Israel accuses the association of financing Hezbollah.
Earlier in the day, the IDF said that dozens of projectiles were fired at northern Israel in the past 24 hours.
It also said that its warplanes conducted “an intelligence-based strike on a command centre of Hezbollah’s intelligence headquarters and an underground weapons workshop in Beirut”.
It said steps had been taken to “reduce the possibility of civilian casualties”.
Israel has been accused by Hezbollah and Lebanese officials of targeting civilians, which it denies.
Earlier on Sunday, the United Nations Interim Force in Lebanon (Unifil) accused the IDF of deliberately demolishing an observation tower and perimeter fence of a UN position in the southern Lebanese town of Marwahin on the border with Israel. It follows similar incidents in recent weeks.
“Yet again, we note that breaching a UN position and damaging UN assets is a flagrant violation of international law and Security Council resolution 1701,” the Unifil said in a statement.
In a separate development, the Lebanese army said three of it soldiers were killed after a military vehicle was hit by an Israeli air strike in Nabatieh, southern Lebanon.
Israel has not yet commented on the two reported incidents.
Lebanon’s army has historically stayed out of cross-border clashes between Israel and Hezbollah – but a number of its troops have been killed in Israeli attacks since fighting escalated last month.
Hezbollah – a powerful militant group in Lebanon – says it has been firing on Israeli positions in solidarity with Hamas in the Gaza Strip.
Both Hezbollah and Hamas are backed by Iran.