"We are actively preparing for the June 12 summit between the president and the North Korean leader", White House spokesperson Sarah Sanders said.
That was the case when Trump recognized a North Korean defector during his State of the Union address in January and hosted a group of North Korean escapees in the Oval Office.
Such matters "need to be embedded in a broader political discussion that encompasses a wide variety of issues", Victor Cha, the top Asia policy official at the National Security Council during President George W. Bush's administration, told lawmakers.
In a remarkable shift in tone eight days after cancelling the summit, citing Pyongyang's "open hostility", Trump welcomed North Korea's former intelligence chief, Kim Yong Chol, to the White House on Friday, afterwards exchanging smiles and handshakes.
There was initially much uncertainty over whether the summit would go ahead at all, and it was briefly called off last month by Mr Trump after a dispute with the North Koreans.
At the April 27 summit between the two Koreas, some observers commented on the unusual sight of members of North Korea's top military brass saluting South Korean president Moon Jae-in.
But after meeting a senior North Korean official in Washington last week, he said he did not want to use the term anymore, because the two sides were "getting along".
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The Hang Seng in Hong Kong slipped 1.5 per cent to 30,034.07 and the Shanghai Composite index fell 1.6 per cent to 3,072.76. Japan's Nikkei 225 slumped 0.9 percent to 22,280.91 while South Korea's Kospi was down 0.7 percent to 2,460.75.
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Assad was quoted as saying: "I am going to visit the Democratic People's Republic of Korea (DPRK) and meet Kim Jong-un ". Yonhap reported that Kim Yong Chol had transited Beijing on Monday on his way back to Pyongyang from the United States.
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The president said the only option to respond to the Israeli attacks is by improving the air defenses and "we are doing that". He rejected Israel's claims last month that it had targeted Iranian troops in Syria as "a lie".
The June summit in Singapore will be an historic one, marking the first meeting between a North Korean leader and a sitting USA president.
"In return, the U.S. seems to be offering to accept more of the North's demands such as declaring an end to the Korean War and taking a step-by-step approach in the denuclearization process", he said.
"A lot of relationships being built, a lot of negotiations going on before the trip", he said.
North Korea made no immediate reference to any military changes, and it remains hard to assess whether the shake-up could signal a significant change in North Korean policies.
It is a shift from the speedy, "all-in-one" denuclearization the U.S. has demanded from North Korea. "They're very powerful, and we would not take those sanctions off unless North Korea denuclearises", she said.
Russian President Putin is scheduled for a three-day state visit to China to attend the Shanghai Cooperation Organization summit in Qingdao, a coastal city in Shandong Province, which takes place on June 9 and 10 and will be chaired by Xi.
Publicly, the cost of dismantling North Korea's nuclear weapons program, and who will cover it, has yet to be discussed by the concerned countries.