Ahead of the summit Mr Trump had said that he was positive on North Korea as long as they weren't testing nuclear weapons or long-range missiles.

He said Mr Kim promised that this would continue.

"One of the things [Mr Kim] promised me last night is... he's not going to do testing," he says. "I want to keep the relationship, we'll see what happens over the next period of time."

Mr Trump explains further:

"He [Kim Jong-un] has a certain vision and its not exactly our vision but it's a lot closer than it was a year ago and I think eventually we'll get there but for this particular visit we decided that we had to walk."

The president is taking questions from reporters now. He's discussing why no deal was made.

"Frankly I think we'll end up being very good friends with chairman Kim," he says. "They have tremendous potential but it was about sanctions... they were willing to give us areas but not the ones we wanted," he added. He said Mr Kim is willing to "de-nuke" in some areas, "but not the areas that we want".

It's unclear what this means but a possible shutdown of North Korea's Yongbyon nuclear site was one of the things analysts expected to be discussed.

"They wanted sanctions lifted in their entirety. We couldn't do that," says Mr Trump.

"I wish we could have got a bit further but I'm still optimistic," said US Secretary of State Mike Pompeo. "I hope we'll do so in the weeks ahead.'

Mr Trump has handed over to his secretary of state, MIke Pompeo. "We asked him to do more, he was unprepared to do that," he says of Mr Kim.

"It wasn't a good thing to be signing anything. We literally just left. We spent pretty much all day with Kim Jong-un."

He says the relationship is very strong but "we decided not to do any of the options".

Mr Trump has started by talking about foreign crises.

The presser has begun. Mr Trump thanks the Vietnamese people.

The press conference was due to start more than 10 minutes ago - no sign yet of Mr Trump.

BBC Monitoring is watching North Korea’s state-run Korean Central Television, which started operations for the day at 06:00 GMT as usual.

From 06:09 GMT onwards, the famous news anchor known as the "Pink Lady", Ri Chun-hee, read out a report about the leader Kim Jong-un’s meeting, one-on-one chat and dinner with Mr Trump last night.

Meanwhile, the Western media is focused solely on today's developments - and the news that there won't be a peace declaration.

Image source, KCNA

Experts are telling the BBC this is likely a serious breakdown in the negotiations between North Korea and the US. Both leaders have a lot to lose from this process falling apart. Will Mr Trump come out shortly and say this is a sign of the US standing up to North Korea?

The summit, as seen by America's news channels.

So why might it have fallen apart? Korea watcher Ankit Panda thinks it may have come down to a disagreement over what to do with North Korea's nuclear power facility Yongbyon. North Korea wants some sanctions relief in exchange for shutting it down. Did Mr Trump refuse to budge on that? We should find out soon - he's due to speak to the press in a few minutes.

North Korean expert Olivia Enos from The Heritage Foundation gives her take to the BBC on the "no deal" outcome:

"It’s better to not sign a deal than to agree to untenable terms and get a bad deal that locks the US and North Korea in a bind. Regardless of the areas of disagreement, the US should continue to press for complete, verifiable, irreversible dismantlement (CVID) of North Korea’s nuclear programme and improvements in human rights. US should continue to hold the line on maximum pressure if and until CVID and human rights improvements are made and agreeable terms can be set."

Here in Hanoi, there is a lot of very quick typing and paper rustling going on. The top of the hour is when most people here go live - and so far few people know what they're going to say on air.