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.

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.

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."

Tehran accused the United States of "excessive demands", Iranian media said on Saturday, as U.S. media reports raised the prospect that Washington was mulling new strikes and leaders of the Islamic republic considered the latest peace proposal.

The Trump administration was preparing Friday for a fresh round of military strikes against Iran, sources with direct knowledge of the planning told U.S. TV network CBS, even as diplomacy continued.

On the surface, Chinese leader Xi Jinping's back-to-back summits with U.S. President Donald Trump and Russia's Vladimir Putin looked pretty similar, with formal handshakes in Beijing's Tiananmen Square, enthusiastic greetings from flower-waving children, and marching columns of soldiers with gleaming bayonets. But the visits also revealed how different China's relationship is with the two countries.

During Trump's visit, China sought to stabilize ties with the United States, while Putin's trip served to deepen its strategic partnership with Russia.