Donald Trump hints 'something positive' on North Korean crisis

US President Donald Trump indicated that a deal could be struck with North Korea over its nuclear weapons programme, soon after his top diplomat said Pyongyang has demonstrated some level of restraint in recent days.

At a rally in Phoenix, Arizona, Trump said he "respects" that North Korean leader Kim Jong-Un "is starting to respect us."

"I respect that fact very much," Trump told the crowd.

"And maybe - probably not - but maybe something positive can come about," he said, but did not explain what kind of an agreement he was expecting to reach with North Korea.

Tensions between the US and the North have been quite high since Pyongyang tested two intercontinental ballistic missiles in July that could reach the US mainland.

In response, the UN Security Council unanimously imposed new sanctions on North Korea on August 5. Trump warned North Korea that if it persisted with its threat to the US it would face "fire and fury" and escalated the rhetoric saying that US military solutions against the North were "locked and loaded."

But last week the North Korean leader backed off from a plan to launch four ballistic missiles towards the American territory of Guam.

Trump's comments today came after Secretary of State Rex Tillerson said the North Korean regime has demonstrated some level of restraint in recent days, "that we've not seen in the past".

"I think it is worth noting that we have had no missile launches or provocative acts from the part of North Korea since the unanimous adoption of the UN Security Council resolution. I want to take note of that. I want to acknowledge it," Tillerson told reporters at a news conference here.

He hoped that this could be the beginning of the signal the US has been looking for.

"Perhaps we are seeing our pathway to some time in the near future to having some dialogue," Tillerson said.

"We need to see more on their part but I want to acknowledge the steps they've taking thus far," he said.