North Korea's rapid progress in developing nuclear weapons and missiles has fueled a surge in regional tensions as United Nations-led sanctions appear to have failed to bite deeply enough to change its behavior.
China and Russia have proposed that the United States and South Korea stop major military exercises in exchange for North Korea halting its weapons programs.
Beijing formally calls the idea the "dual suspension" proposal.
Speaking upon his return from Asia on Wednesday, Trump said he and Xi had agreed that they would not accept a "freeze for freeze" idea, which China's foreign minister announced in March.
Asked how China understood Trump's remarks and whether he agreed with the characterization of what Trump said he agreed to with Xi, Chinese Foreign Ministry spokesman Geng Shuang said only through talks that addressed all sides' legitimate security concerns could there be a peaceful resolution.
"We believe that the 'dual suspension' proposal is the most feasible, fair and sensible plan in the present situation," Geng told a daily news briefing.
"Not only can it relieve the present tense situation, it can also resolve all parties most pressing security concerns, and provide an opportunity and create conditions to resume talks, and find a breakthrough point to get out of trouble," he added.
"We hope that all sides can conscientiously treat and proactively consider China's proposal, and at the same time we welcome relevant parties to put forward proposals that can benefit the promotion of a peaceful resolution for the peninsula nuclear issue."
Asked at a regular briefing if Trump stood by his remarks as to what he had agreed with Xi, White House spokeswoman Sarah Sanders on Thursday replied: "Both sides made their positions clear. They are different, but we agreed that there are going to be different positions and therefore it's not going to move forward."
North Korea has said it needs to develop its weapons to protect itself from what it sees as U.S. military aggression. It also sees U.S.-South Korean military exercises as joint preparations for invasion.
South Korea and the United States, which has about 28,000 troops based in South Korea, say their exercises are "defensive in nature."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)