North Korea has repeatedly called for an end to large-scale joint military exercises between the allies in exchange for a freeze on its nuclear and missile programmes.
Annual military drills involving tens of thousands of United States and South Korean troops are due to begin on Monday.
China is telling the US and North Korea to "hit the brakes" on threatening words and actions and work toward a peaceful resolution of their dispute, in a sign of growing concern over the standoff on the part of Pyongyang's only major ally.
Dunford on Tuesday told Fang Fenghui, chief of the People's Liberation Army's joint staff department, that the sides had "many hard issues" between them but were willing to deal with them through dialogue.
Fan Changlong, a vice chairman of China's powerful Central Military Commission, told his American counterpart that military means should not be an option in solving the Korean Peninsula issues.
Though the Xi government has expressed its resolve to recover bilateral relations since Moon took office in May, its economic retaliation and diplomatic pushback have shown few signs of abating.
The annual drills - described as defensive and named after a general who protected an ancient Korean kingdom from Chinese invaders - will involve about 50,000 South Korean and 17,500 United States troops, Seoul's defence ministry said Friday.
"To ease the tense situation created by tit-for-tat escalations, to halt this vicious cycle, there is a need to put aside the dispute over who goes first and who goes second", she said, speaking at a regular briefing.
The North said the Guam missile strike could be reinstated in the event of "reckless actions" by Washington, and analysts say the exercise could become an alarming flash point.More news: CSU, Chico to Host Physics Experts for Solar Eclipse Viewing Party
"I say this with confidence that there will be no war on the Korean Peninsula ever".
In the early 1990s Seoul and Washington agreed to cancel a drill then known as Team Spirit in return for the North allowing an inspection of its secret nuclear facilities - only to see Pyongyang later walk away and resume its weapons development.
United States and South Korean officials have for months been expecting a sixth nuclear test.
"The US and President Trump promised no matter what options they use, they will sufficiently consult with South Korea and get consent".
Conservative politicians have urged the ruling liberal Democratic Party to beef up South Korea's military defences to counter the escalating threat from the North.
"China insists that consultation through dialogue is the only effective way to solve the problems on the peninsula, and military means can not be an option", Fan said when meeting with Dunford.
Bannon said he was pushing the USA administration to take a harder line on China trade and not put complaints against its trade practices in the back seat in the hope it would help restrain the North's leader, Kim Jong Un. "And we have to be maniacally focused on that", The American Prospect quoted Bannon as saying.
The visit to the Strategic Force of the Korean People's Army, during which Kim praised it for its preparedness for "enveloping fire at Guam", marks his first appearance in the country's official media reports in about two weeks.
Trump tweeted that Kim a had "made a very wise and well reasoned decision". "The alternative would have been both catastrophic and unacceptable!"