US President Donald Trump tempered expectations of a Middle East deal by saying on Sunday he had told his negotiators not to "rush," even after both Tehran and Washington signalled progress towards an agreement to end the war.

The United States and Iran have observed a ceasefire since 8 April while mediators push for a negotiated settlement, although Iran has imposed controls on Gulf shipping and the US has blockaded Iran's ports.

The war erupted after the United States and Israel attacked the Islamic republic on 28 February and Iran responded with missile and drone attacks across the region.

"I have informed my representatives not to rush into a deal in that time is on our side," Trump said in a social media post Sunday.