U.S. President Donald Trump and North Korean leader Kim Jong-un struck a positive tone as they begin their second summit in Vietnam.

The two leaders exchanged handshakes, laughs and some small talk Wednesday at the Sofitel Legend Metropole Hanoi.

"I thought the first summit was a great success and I think this one, hopefully, will be equal or greater than the first," Trump told reporters.

Speaking through an interpreter, Kim said Wednesday he is "confident of achieving the great results that everyone will welcome" during the summit.

Asked whether he might formally end the Korean War, he responded: "We'll see."

Watch as Trump outlines his expectations for his meeting with Kim:

The U.S. president and North Korean leader met for their second face-to-face summit in Vietnam. 0:29

The two leaders and their top advisers then held what the White House was calling a "social dinner" at the hotel. On the menu at the 90-minute dinner was shrimp cocktail with Thousand Island dressing, marinated grilled sirloin with pear kimchi, chocolate lava cake with berries and vanilla ice cream, as well as dried persimmon punch, which the White House described as a traditional beverage sweetened with dried persimmons and honey.

The White House did not immediately provide more information on the dinner, which had restricted media access.

Trump and Kim are scheduled to hold additional meetings with aides on Thursday before Trump returns to the U.S.

Anticipation high in Hanoi

Anticipation for what will come out of the summit is running high in Hanoi. But the carnival-like atmosphere in the Vietnamese capital, with street artists painting likenesses of the leaders and vendors hawking T-shirts emblazoned with their faces, stands in contrast to the serious items on the agenda: North Korea's pursuit of nuclear weapons and peace on the Korean Peninsula.

Trump told Vietnam's top leaders that Kim could use Vietnam as a model for economic revitalization. "If you look at what you've done in a short time, he can do it in a very, very rapid time — make North Korea into a great economic power."

The president sounded a similar message about Vietnamese prosperity in a tweet before he left his heavily guarded hotel.

"Vietnam is thriving like few places on earth. North Korea would be the same, and very quickly, if it would denuclearize," Trump tweeted Wednesday, hours before he and Kim were to meet again. "The potential is AWESOME, a great opportunity, like almost none other in history, for my friend Kim Jong Un. We will know fairly soon - Very Interesting!"

Trump said at a separate meeting with Vietnamese officials that "hopefully great things will happen later on with our meeting" with Kim.

Trump and Kim first met last June in Singapore, a summit that was long on historic pageantry but short on any enforceable agreements for North Korea to give up its nuclear arsenal. North Korea has spent decades, at great economic sacrifice, building its nuclear program, and there is widespread skepticism that it will give away that program without getting something substantial from the U.S.

That could be a declaration to end the Korean War. Such an announcement would allow Trump to make history and would dovetail with his opposition to "forever wars." But it wouldn't amount to concrete steps toward denuclearization and could even turn the focus of discussions to removing or reducing the 28,500 U.S. troops stationed in South Korea. If there is no war, North Korea could ask why the U.S. needs to have troops in South Korea at all.

The conflict ended in 1953 with an armistice, essentially a ceasefire signed by North Korea, China and the 17-nation, U.S.-led United Nations Command. If made, the declaration would amount to a political statement, ostensibly teeing up talks for a formal peace treaty that would involve other nations.

While Trump wants Kim to agree to dismantle his nuclear sites in a verifiable way, Kim is seeking relief from crushing U.S. sanctions hobbling his economy. Trump has been using Kim's need for economic revitalization as leverage to get concessions on denuclearization.

Vietnamese policemen stand guard outside Melia hotel ahead of the North Korea-U.S. summit in Hanoi. (Kim Kyung Hoon/Reuters)

Other items being discussed are opening liaison offices in both North Korea and the United States. North and South Korea also want sanctions dialed back so they can resurrect two major symbols of rapprochement that provided much-needed hard currency to North Korea: a jointly run factory park in Kaesong and South Korean tours to the North's scenic Diamond Mountain resort.

Trump remains eager to claim an attention-grabbing victory at the summit to offset the political turmoil he faces at home.

With the president away from the U.S., his now-disbarred former personal lawyer was testifying publicly on Capitol Hill later Wednesday about alleged misconduct by Trump. The Democratic-led House, with backing from several Republicans, approved legislation aimed at blocking the Republican president from steering billions of dollars to build barriers along the U.S.-Mexico border. A House committee also voted to subpoena administration officials over family separations at the border.

Michael Cohen, once Trump's loyal attorney and fixer, has turned on his former boss and co-operated with special counsel Robert Mueller, who is looking into whether the Trump's presidential campaign co-ordinated with Russia and whether the president tried to obstruct the investigation.

The president's eldest son, Donald Trump Jr., accused Democrats in Congress of scheduling Cohen's testimony to overshadow the summit.

"After 60 years of failed attempts trying to end the war, trying to end nuclear proliferation on the Korean peninsula, you have finally a president who's willing to do it," he told Fox News Channel. "For the Democrats to try to counter-program that kind of progress — to try to perhaps somehow distract him with this nonsense ... it just goes to show you how much those Democrats really disdain Trump but also America."

The president jabbed at Democrats too, saying in a tweet that they "should stop talking about what I should do with North Korea and ask themselves instead why they didn't do 'it' during eight years of the Obama Administration?"