Trump has said he could meet with Kim in late May or June.
The United States is pressing North Korea to give up its nuclear weapons and says it will keep up a policy of "maximum pressure" on Pyongyang through sanctions to achieve this goal.
Trump said he hoped dealings with North Korea would be positive, but he wanted to see the country's complete denuclearisation.
"It means they get rid of their nukes," he said, when asked to clarify what that meant. "Very simple ... it would be very easy for me to make a simple deal and claim victory. I don't want to do that. I want them to get rid of their nukes."
Trump said he would not repeat the mistakes of past administrations, which his aides have accused of relaxing sanctions too early in pursuit of deals with North Korea.
"The campaign of maximum pressure will continue," Trump said.
"The end result is, we'll see. Maybe good things will happen; it may be we're all wasting a lot of time, but hopefully it will all be good for everybody concerned."
South Korean President Moon Jae-in, who is due to meet Kim in a summit on Thursday, said last week that North Korea had expressed a commitment to "complete denuclearisation", and Pyongyang said on Saturday it would immediately suspend nuclear and missile tests.
This has eased concerns that North Korea could quickly complete development of nuclear missiles capable of hitting the United States.
However, many experts have expressed doubt that Kim will be willing to abandon a weapons program he sees as essential to the survival of his ruling family dynasty.