The White House has barred reporters who asked questions of a "sensitive nature" from covering a dinner between US President Donald Trump and North Korean leader Kim Jong-un.

Key points: Mr Trump was asked if he had a reaction to Mr Cohen's testimony

Mr Trump was asked if he had a reaction to Mr Cohen's testimony A White House spokeswoman said there were "sensitivities over shouted questions"

A White House spokeswoman said there were "sensitivities over shouted questions" Steak and kimchi were prepared by North Korean chefs for the leaders' dinner

During the opening of the second summit between the two leaders in Vietnam's capital, Hanoi on Wednesday, reporters had asked Mr Trump about the testimony in Congress of his former attorney and fixer Michael Cohen.

Reuters, the Associated Press and Bloomberg are part of the White House press pool that covers US presidents wherever they go. Reporters in the pool regularly shout out questions to leaders.

The reporters were later excluded from covering the dinner because of what White House spokeswoman Sarah Sanders said were "sensitivities over shouted questions", the Washington Post reported.

The second summit between Donald Trump and Kim Jong-un is being held in Hanoi. ( Reuters: Leah Millis )

The two leaders launched the summit with broad smiles as they shook hands for the cameras before heading to dinner at the Sofitel Legend Metropole hotel in the centre of Hanoi.

"A lot of things are going to be solved I hope," Mr Trump said. "I think it will lead to a wonderful, really a wonderful situation long-term."

He said he looked forward to helping Mr Kim achieve a "tremendous" economic future for his country.

Mr Kim, whom the US President described as a "great leader", said he was confident there would be an "excellent outcome that everyone welcomes".

"I'll do my best to make it happen," he told reporters, before the men sat down to eat.

'Sensitivities over shouted questions'

During Mr Trump and Mr Kim's initial meeting, Reuters correspondent Jeff Mason and AP reporter Jonathan Lemire questioned Mr Trump about his commitment to denuclearisation and whether he expected to end the Korean War to which Mr Trump said: "We'll see."

Mr Lemire later asked Mr Trump if he had a reaction to Mr Cohen's testimony, in which the President's former lawyer called Mr Trump a racist, a conman and a cheat.

Mr Trump scowled and shook his head.

The two reporters were then excluded from attending the dinner along with two others.

"Due to the sensitive nature of the meetings we have limited the pool for the dinner to a smaller group, but ensured that representation of photographers, TV, radio and print poolers are all in the room," Ms Sanders said in a written statement.

The agencies said they were "deeply troubled" by the exclusion.

"We believe it is essential that government provide access to and the ability to ask questions of officials and hold them to account," Reuters said in a statement.

AP spokeswoman Lauren Easton said: "It is critically important that any president uphold American press freedom standards, not only at home but especially while abroad."

Steak, kimchi and lava cake

Chefs from North Korea worked together with staff at the colonial-era hotel to create a medley of Western and Korean dishes for the two leaders. ( AP: Evan Vucci )

Chefs from North Korea worked together with staff at the colonial-era hotel to create a medley of Western and Korean dishes for the two leaders.

The blend included two American and two Korean dishes, according to a copy of the menu released by the White House late on Wednesday.

The two Western dishes, a shrimp cocktail and a "hot and runny-centred" chocolate lava cake, were created by chefs at the hotel, sources said.

The two Korean dishes — grilled steak with a pear kimchi and a non-alcoholic dried persimmon punch digestif — were prepared by North Korean chefs specially brought in for the event.

Mr Trump tweeted that he had a "very good dialogue" with North Korean leader.

"Great meeting and dinner with Kim Jong Un in Hanoi, Vietnam tonight," Mr Trump said in a message on Twitter at the end of the first day of their second summit.

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Mr Kim told reporters that his country had long been "misunderstood" and viewed with "distrust".

"There have been efforts, whether out of hostility or not, to block the path that we intend to take," he said.

"But we have overcome all these … and we have met again here and I am confident that we can achieve great results that everyone welcomes."

The two leaders will hold a 45-minute one-on-one meeting on Thursday followed by expanded talks involving their aides and a "joint agreement signing ceremony" at the end of their summit in Vietnam on Thursday, the White House said.

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ABC/wires