Israel gave the United States a document last week with its conditions for a diplomatic solution to end the war in Lebanon, Axios reported, citing two US officials and two Israeli officials.
Israel has demanded its forces be allowed to engage in "active enforcement" to make sure Hezbollah doesn't rearm and rebuild its military infrastructure close to the border, Axios reported, citing an Israeli official.
Israel also demanded its air force have freedom of operation in Lebanese air space, the report added.
A US official told Axios it was highly unlikely that Lebanon and the international community would agree to Israel's conditions.
The White House could not be immediately reached outside regular business hours. The US State Department did not immediately respond to a request for comment.
The embassies of Israel and Lebanon in Washington did not immediately respond to a request for comment.
White House special envoy Amos Hochstein is visiting Beirut on Monday to discuss a diplomatic solution to the conflict, the report added.
Ukrainian President Volodymyr Zelenskyy marked Independence Day on Sunday alongside Canadian Prime Minister Mark Carney, who said Ukraine would receive more than C$1 billion ($723 million) in military aid from a previously announced package next month.
Israeli planes and tanks pounded the eastern and northern outskirts of Gaza City overnight Saturday to Sunday, destroying buildings and homes, residents said, as Israeli leaders vowed to press on with a planned offensive on the city.
The Pentagon is working on plans to deploy the US military to Chicago as President Donald Trump says he is cracking down on crime, homelessness and undocumented immigration, the Washington Post reported on Saturday.
Thousands of Australians joined pro-Palestinian rallies on Sunday, organisers said, amid strained relations between Israel and Australia following the centre-left government's decision to recognise a Palestinian state.
North Korean leader Kim Jong Un supervised the firing of new air defence missiles to test their combat capability, state media KCNA reported on Sunday.