Israel launched fresh strikes on Beirut's southern suburbs late Sunday as Israel's military said it was striking Hezbollah infrastructure in the city following earlier raids mainly in the country's south.

A midnight strike, heard in the capital, came after a morning Israel army evacuation warning for Beirut's southern suburbs, which Israel has repeatedly struck in the past fortnight.

The Israeli military said on Monday it had begun what it described as "limited ground operations" against Hezbollah in southern Lebanon.

"In recent days, IDF troops from the 91st division have begun limited and targeted ground operations against key Hezbollah strongholds in southern Lebanon, aimed at enhancing the forward defense area," the military said in a statement.

Daily contacts are taking place between Israel and Lebanon with U.S. and French mediation, the Israel Hayom newspaper has reported.

Mahmoud Qmati, the deputy head of Hezbollah's Political Council, has rejected the reported French proposal to end the war between his group and Israel, saying it was "born dead."

Israel said on Sunday that no direct talks were planned with Lebanon to end the war, a day after a Lebanese official said Beirut was preparing a delegation to negotiate with Israel.

Israeli Prime Minister Benjamin Netanyahu's envoy, ex-minister Ron Dermer, has recently visited Saudi Arabia and spoke with senior officials in the kingdom about a renewed initiative for an arrangement in Lebanon, the Israeli army radio reported on Sunday.

Overnight strikes in southern Lebanon killed at least four people, Lebanese state media and the government said on Sunday, as Israel said it was pressing its campaign against Iran-backed Hezbollah.

Hezbollah said it was involved in "direct clashes" with Israeli forces in the southern Lebanese town of Khiam late on Saturday.

In a statement, it said the clashes were ongoing, having started at 9:20 pm (1920 GMT) and involved "light and medium weapons as well as rocket-propelled projectiles".

France's foreign ministry said Saturday there was "no French plan" to stop the fighting in Lebanon between Israeli forces and Iran-backed militant group Hezbollah.

U.N. chief Antonio Guterres said Saturday on a visit to Beirut that diplomatic channels remained open to end the war between Israel and Hezbollah and urged the international community to support Lebanon.