Graham's remarks echoed those of McMaster, who told a security forum in Washington on Saturday that the potential for war with North Korea "is increasing every day".
His comments came three days after North Korea carried out its first ballistic missile test in two months, in defiance of United Nations resolutions. China is North Korea's only significant ally, but it has grown increasingly frustrated over the North's nuclear and missile tests that have brought a threat of war and chaos to China's northeastern border.
It was the country's third intercontinental ballistic missile (ICBM) test, but the first of what North Korea is calling its Hwasong-15 missile.
That sparked a strong rebuke Friday from Russia's Foreign Minister Sergey Lavrov.
The United States has demanded tougher worldwide sanctions in response to the latest missile tests, including cuts in oil shipments to the isolated state.
Amid concerns about the tenuous situation that has been exacerbated by heated exchanges between US President Donald Trump and North Korean officials could lead to a military path, Bessho stressed that changing the North's policy is the point of emphasis.
Russian Federation and China have proposed a roadmap for defusing the crisis in the region.
He responded "I don't think so" when asked whether the Mueller probe affected American allies. It has been set up under the South Korean army's Special Warfare Command.
The commentary was published a day after Pyongyang's foreign ministry accused the Trump administration of "begging for nuclear war" by staging what it called the reckless air drills.
A Foreign Ministry spokesman said that the United States is planning to carry out the largest-ever joint aerial drill with South Korea targeting the DPRK from December 4 to 8, which he said will push the current touch-and-go situation in the peninsula to a possible flare-up.
Vice Chairman Pak Kwang-Ho of the party's decision-making Central Committee told the crowd that, after Wednesday's test launch, "now no one can infringe our sovereignty and rights to survive and develop", according to the daily.
He repeated Kim's warning that the North would respond with the "highest level of hard-line countermeasure in history".
The ICBM Hwasong-15 type weaponry system used in Wednesday's test is an intercontinental ballistic rocket tipped with super-large heavy warhead capable of striking the whole mainland of the U.S., the North said.