Im added it would be necessary for South Korea and the U.S. to hold a summit after President Moon Jae-in's meeting with North Korean leader Kim Jong-un - a measure that Im said would help both Washington and Pyongyang narrow gaps before the planned summit to be held by May.
While pledging to keep maximum pressure on Pyongyang, Trump and Moon "expressed cautious optimism over recent developments and emphasized that a brighter future is available for North Korea, if it chooses the correct path", it said.
South Korea's foreign ministry tweeted a photo of their reunion on Thursday, showing the pair seated at a large round table with bread and flowers.
Foreign Minister Ri Yong Ho landed at Stockholm's Arlanda airport on a direct flight from Beijing late Thursday and spent several hours at the Swedish Foreign Ministry before returning to the North Korean Embassy.
North Korean state media confirmed Ri's trip on Friday, saying he had flown to Sweden to speak with his counterpart on "bilateral relations and issues of mutual concern".
Japan's Kyodo news agency said Saturday the minister made therequest during his meeting with U.S. Vice President Mike Pence at the WhiteHouse on Friday.
However, in the light of the diplomatic thaw with Pyongyang, South Korea and the USA will scale down and shorten annual joint military exercises.
Yun said he had delivered the message in talks with North Korean officials after Trump's announcement last week that he would be willing to meet face-to-face with Kim.
Since this would happen at the highest level of negotiations, there'd be no fallback position or further negotiations for the U.S. The only remaining option would be military intervention, which would be inevitable and turn the world against us as the aggressor, done only to protect our military presence in South Korea.
"We are hoping that if we can use our role and also our contacts, then we will put them to the best use". -North Korean summit during seven decades of hostility since the 1950-53 Korean War.
"The aim of the visit is to contribute to the effective implementation of the resolutions" voted by the Security Council against Pyongyang over its nuclear programme as well as those calling "for intensified diplomatic efforts to find a peaceful solution to the conflict".
U.S. President Donald Trump has accepted an invitation to meet with Kim Jong Un to negotiate Pyongyang's nuclear program.
Mr Im added that Mr Moon may meet Mr Trump after the inter-Korean summit, but before Mr Trump's planned summit with Mr Kim in May.
Worldwide media have speculated that Sweden could be a potential location if the summit were to be confirmed.
So the visit has prompted speculation it might be part of preparations for the US-North Korea summit.
Kang is also on a three-day visit to the US capital through Saturday.