U.S. President Donald Trump has assured Israeli Prime Minister Benjamin Netanyahu he will hold firm on his demand for the dismantling of Iran's nuclear program as a condition in any final agreement with Tehran, a senior Israeli official told AFP on Sunday.

Israeli strikes hit Lebanon on Sunday, both before and after Israel's military issued an evacuation warning for 10 villages in the south and east, state media reported.

U.S. President Donald Trump said Sunday that he had told U.S. negotiators "not to rush into a deal" with Iran, amid anticipation that an agreement to end the war in the Middle East was close.

"The negotiations are proceeding in an orderly and constructive manner, and I have informed my representatives not to rush into a deal in that time is on our side," Trump wrote on his Truth Social account.

Lebanon's civil defense agency said early on Sunday its regional facility in the southern city of Nabatieh had been destroyed by an Israeli strike.

Israel struck south Lebanon on Saturday despite a ceasefire as Hezbollah said its backer Tehran had pledged not to abandon the militant group.

Pakistan's Prime Minister Shehbaz Sharif said on Sunday he hoped his country could soon host the next round of peace talks between Iran and the United States.

U.S. Secretary of State Marco Rubio said an announcement was possible later Sunday on a deal with Iran that could formally end the Middle East war, insisting goals had been met.

The United States and Iran could strike a deal to end the Middle East war as early as Sunday, Washington's top diplomat said, while Tehran insisted the agreement would do nothing to limit its nuclear program.

A gunman opened fire near the White House on Saturday evening, with U.S. Secret Service agents killing the assailant in a shoot-out during which a bystander was also struck, authorities said.

U.S. President Donald Trump said Saturday a deal with Iran had been "largely negotiated," with the proposal including opening the crucial Strait of Hormuz, though the agreement was "subject to finalization."