The discussions will put a heavy emphasis on stopping North Korean money laundering as well as smuggling by sea, which USA officials have suggested could involve taking action against North Korean shipping.
On Thursday, Trump suggested in an interview with The Wall Street Journal that he could have a good relationship with Kim, though he left vague the extent of his dealings with the North Korean leader.
"I have relationships with people".
"I think that they will continue to develop their nuclear and missile capability".
The paper reported that Trump would not say whether contacts had already been initiated between the two foes.
The gathering comes as tensions have sharply escalated over North Korea's provocations, which past year included its sixth nuclear test and three tests of intercontinental ballistic missiles.
The meeting is to be co-hosted by the United States and Canada next Tuesday in Vancouver.
He also said the meeting does not involve all the key countries related to the North Korean nuclear issue.
Hook, meanwhile, defended the decision not to invite China and Russian Federation to Vancouver, which State Department under-secretary Steven Goldstein later said was made in conjunction with Canada.
One of the options to be discussed, he said, would be naval interdiction to stop North Korean smuggling.More news: Who Is Headlining Firefly Music Festival 2018?
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According to Bloomberg News, a Japanese foreign ministry official recently questioned the need for including countries as distant as Colombia and Greece.
But while Canada and the USA have welcomed the Korean discussions, Hook said they were unlikely to change the agenda of the Vancouver meeting or result in a short-term softening of sanctions.
Pyongyang also agreed to send its high-ranking delegation and athletes to the 2018 Winter Olympic and Paralympic Games, which are set to run from February to March in South Korea's eastern county of PyeongChang.
"And maritime interdiction helps us to disrupt resources and then the financial side helps us to disrupt the financing of their nuclear and missile program".
More curious is the summit's guest list, made up of so-called "sending countries" that contributed troops to the United Nations force in the Korean War.
Western security officials have accused Russian Federation and China of exporting oil to North Korea in recent months, which would be a violation of United Nations sanctions.
But Hook said Washington remained in contact with China about enforcing the sanctions and pressuring Kim, and that both Beijing and Moscow would be briefed after the talks.
"China is working with us". "This is not an alternative to everything that we are doing".
"This ministerial will enhance and strengthen all of the efforts underway to achieve our policy goals", he said.
"China is very reluctant to attend meetings about North Korea that don't include North Korea".