Nikki Haley, the US's ambassador to the United Nations, last week cast the new sanctions as a victory, but said the USA does not "take pleasure in further strengthening sanctions".
Suga also welcomed Trump's reference to a Japanese girl who was kidnapped by North Korean agents in 1977.
While acknowledging that China is not responsible for the crisis, the United States, nevertheless, is leaning heavily on it to check North Korea.
In the aftermath of the North's most recent test, talk of redeploying nuclear weapons in South Korea became more frequent, with conservatives and liberals alike offering their support to the idea.
The ministry said that the worldwide community is sternly responding to North Korea's provocations, but also emphasizing the need to extend humanitarian assistance to North Koreans.
North Korea, which has conducted more than 80 missile tests under third-generation leader Kim, says it needs its weapons to protect itself from US aggression.
In May, Seoul announced its move to spur civilian inter-Korean exchanges and assistance, but North Korea has rejected them, citing the South's support of United Nations sanctions.
Worldwide tensions were then increased when Pyongyang launched a second ballistic missile across Japan two weeks later.
The fall is believed to be a result of tighter government surveillance and reinforced border security by both North Korea and China, to where most people go before reaching South Korea.
He says the USA should consider China's suggestion to halt military exercises with South Korea, in exchange for North Korea freezing its nuclear and missile tests.
The decision to send aid to North Korea was not popular in South Korea, hitting President Moon Jae-in's approval rating. That is why South Korea's President Moon Jae In dashed to Russian Federation recently to seek help.
Japan, a key ally of the U.S. facing increasing threats from North Korea, is also expected to take part in a combined drill with the USA supercarrier.
Analysts say North Korea looked at the fate of other authoritarian regimes, particularly Libya under Moammar Gadhafi and Iraq under Saddam Hussein, and concluded that their lack of nuclear weapons left them vulnerable to being toppled by the USA and its allies.
The discussion of whether to shoot down a North Korean missile comes as United States intelligence has assessed that North Korea's KN-17 (Hwasong 12) intermediate range ballistic missile has proven so successful in recent flight tests that Pyongyang now counts on it as part of its strategic deterrence against the USA, according to a U.S. official familiar with the latest intelligence analysis.