"And we have to be maniacally focused on that", The American Prospect quoted Bannon as saying.
A military solution would be "absolutely horrific", Dunford told reporters after the meetings, according to The Associated Press.
Coinciding with Dunford's visit, the USA and Chinese militaries signed an agreement to establish a mechanism for communication between the countries' joint staffs. Xi praised the arrangement, saying it will play a positive role in improving bilateral relations.
He said the military was developing "credible, viable military options" upon orders from Trump.
U.S. Chairman of the Joint Chiefs of Staff Gen. Joseph Dunford (left) shakes hands with Chinese Northern Theater Command Commander Gen. Song Puxuan following a meeting together at Northern Theater Command Army Force Haichung Camp in Haichung, China.
While in Beijing, Dunford will also meet Chinese officials to discuss US-China military cooperation and the Korean Peninsula situation.
Arriving in Tokyo on Thursday, the new USA ambassador to Japan, William Hagerty, said America's ability to defend itself and its allies against North Korea was "beyond question".
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South Korean President Moon Jae-in, meanwhile, a liberal who favors engagement with the North, urged North Korea to stop provocations and to commit to talks over its nuclear weapons program.
North Korea's military on Tuesday presented leader Kim Jong Un with plans to launch missiles into waters near the USA territory of Guam and "wring the windpipes of the Yankees", even as both Koreas and the United States signaled their willingness to avert a deepening crisis, with each suggesting a path toward negotiations.
"My advice to our leadership is that we not dial back our exercises", he said. "I say with confidence that there will never be another war on the Korean Peninsula".
Gen. Fan Changlong, a vice chairman of China's Central Military Commission, spoke with Dunford before the meeting with Xi.
"What person would think right now, holding a military exercise on the doorstep of a madman living in North Korea is not going to put us all in danger?" "I want to warn North Korea to do no more risky gambling", added Moon.
That has heightened fears that this year's UFG exercise may spark a new crisis after North Korean leader Kim Jong Un left open a threat to fire missiles into waters near Guam, saying he would hold off for now while monitoring USA behavior. "The alternative would have been both catastrophic and unacceptable!" Neither the one next week or a large one usually held in March would impact USA readiness, and they could be replaced with more targeted drills that focus on command and control systems, he said. "Regardless of whatever twist and turns we could experience, the North Korean nuclear program should absolutely be solved peacefully, and the (South Korean) government and the USA government don't have a different position on this".
"As long as the threat in North Korea exists, we need to maintain a high state of readiness to respond to that threat".
China, US agree to boost military ties amid North Korea crisis
Tensions have since eased somewhat since North Korea said Kim doesn't immediately plan to fire the missiles. Song Puxuan (center) at Northern Theater Command Army Force Camp in Haichung, China on Wednesday.
The liberal leader has been largely sidelined in recent weeks as Trump and the North engaged in a war of words.
Formal talks on North Korea's nuclear program collapsed in 2009, and the US has resisted restarting them until Kim demonstrates a commitment to denuclearization and halts tests of missiles and nuclear devices. They could be reduced if North Korea were to pursue denuclearization and cease ballistic missile tests, he said.
Moon said he believes the two Koreas must restart a dialogue, but it will take time.
"You are the first senior military official to visit China since US President Donald Trump took office", Xi told Dunford.
Foreign Minister Taro Kono said in Washington Japan would strengthen its defense posture in response to the North Korean threat and provide $500 million to help boost maritime security in East Asia, where China has been pursuing extensive maritime claims that have angered regional neighbors.
"The government, putting everything on the line, will block war by all means", Moon said. Pyongyang eventually reneged on an agreement to dismantle its nuclear reactors - one among many reasons the US doesn't trust North Korea.
Stop the threats, China tells US, North Korea
The U.S. has missile defenses on Guam, at sea and in the continental U.S. that are created to shoot down ballistic missiles. It also could mean the B-1B bombers that the US occasionally flies over the Korean Peninsula as a show of force.