Trump's comments came after a series of social media posts in which he touted progress on reopening the Strait of Hormuz and ending Iran's nuclear program.

"We're very close. Looks like it's going to be very good for everybody. And we're very close to having a deal," Trump said in a brief telephone call with AFP from Las Vegas.

"The strait's going to be open, they already are open. And things are going very well."

A first round of US-Iran talks in Pakistan last weekend ended without a peace deal, but Trump has said a second round could happen soon.

Trump has said the core US demand is that Iran should never be able to develop a nuclear weapon, and he said on Thursday that Iran had agreed to turn over its stock of enriched uranium.

Asked what the remaining sticking points for a deal were, Trump replied, "No sticking points at all."

When asked why he was unable to declare a deal at this point after his string of optimistic posts, Trump said he wanted an agreement on paper.

"I don't do that, I get it in writing," Trump added.