"I'd like to meet him this year," Trump told reporters in the Oval Office as he welcomed South Korea's new President, Lee Jae Myung, to the White House.
"I look forward to meeting with Kim Jong Un in the appropriate future."
Trump and Lee held their first meeting in tense circumstances.
The US president lodged vague complaints about a "Purge or Revolution" in South Korea on social media before later walking the comments back as a likely "misunderstanding" between the allies.
Despite clinching a trade deal in July that spared South Korean exports harsher US tariffs, the two sides continue to wrangle over nuclear energy, military spending, and details of a trade deal that included $US350 billion ($A539 billion) in promised South Korean investments in the United States.
North Korea's rhetoric has ramped up, with Kim pledging to speed his nuclear program and condemning joint US-South Korea military drills.
Over the weekend, Kim supervised the test firing of new air defence systems.
Since Trump's January inauguration, Kim has ignored Trump's repeated calls to revive the direct diplomacy he pursued during his 2017-2021 term in office, which produced no deal to halt North Korea's nuclear program.
In the Oval Office, Lee avoided the theatrical confrontations that dominated a February visit by Ukrainian President Volodymyr Zelenskiy and a May visit from South African President Cyril Ramaphosa.
Lee, deploying a well-worn strategy by foreign visitors to the Trump White House, talked golf and lavished praise on the Republican president's interior decorating and peacemaking.
He told reporters earlier that he had read the president's 1987 memoir, "Trump: The Art of the Deal," to prepare.
As the leaders met, the liberal South Korean encouraged Trump to engage with North Korea.
"I hope you can bring peace to the Korean Peninsula, the only divided nation in the world, so that you can meet with Kim Jong-un, build a Trump World (real-estate complex) in North Korea so that I can play golf there, and so that you can truly play a role as a world-historical peacemaker," Lee said, speaking in Korean.
South Korea's economy relies heavily on the US, with Washington underwriting its security with troops and nuclear deterrence.
Trump has called Seoul a "money machine" that takes advantage of American military protection.
Trump is pressing South Korea on the trade deal they already reached and over a number of issues related to the countries' military alliance.
He also said he would raise with Lee "intel" he had received about investigations in that country that he said targeted churches and a military base.
The White House did not respond to a request for more information.
Earlier this month, Seoul police raided Sarang Jeil Church, headed by evangelical preacher Jun Kwang-hoon, who led protests in support of ousted South Korean President Yoon Suk Yeol.
The police were investigating pro-Yoon activists who stormed a court in late January after it extended Yoon's detention over his December attempt to declare martial law.
In July, prosecutors investigating Yoon's actions served a search warrant on the Korean part of a military base jointly operated with the United States.
South Korean officials have said that US troops and materials were not subject to the search.
Members of Korea's far-right movement, especially evangelical Christians and supporters of Yoon, see the ex-president as the subject of communist persecution.
Trump is expected to pressure Lee to commit to more spending on defence, including toward the upkeep of the 28,500 American troops stationed in South Korea.
