Trump has threatened to cut off trade with all countries that do business with North Korea, a group that includes China. "We'll see what happens", Trump said when asked if he was still considering military action.
"We should not give in to emotions and push Pyongyang into a corner", he said.
The White House on Wednesday released details of calls Tuesday with British Prime Minister Theresa May and Australian Prime Minister Malcolm Turnbull.
While Seoul's military says its missiles are currently capable of wiping out North Korean structures on land, it says heavier warheads are needed to target North Korea's underground facilities and bunkers.
Trump described Pyongyang as a "rogue nation" which had become a "great threat and embarrassment" to China - North Korea's main ally.
The broadcaster said the nuclear test had an "unprecedentedly large power", and that it "marked a very significant occasion in attaining the final goal of completing the state nuclear force".
Diplomats have said the Security Council could consider banning North Korean textile exports, barring its airline and stopping supplies of oil to the government and military.
Trump is to speak Wednesday with China's president. Nonetheless, the nature of China's involvement in any potential conflict will likely depends on how the fighting starts, specifically which country initiates the conflict. It took 82 days for the UN Security Council to adopt Resolution No. 2321 in response to North Korea's fifth nuclear test in Sept. 2016. It also flies to Vladivostok in Russia.
This shift right by the liberal Moon underscores deep unease that the North's expanding nuclear weapons arsenal will undermine the country's decades-long alliance with the United States.
The test unleashed a powerful 6.3-magnitude tremor which was felt across the border in China.
Japanese envoy Koro Bessho said: "We stresses the need for the council to adopt swiftly a new resolution with further robust sanction measures".
There is a history of constructive interaction with the North Korean leadership.
Until August, Kawai served as a special adviser to Abe, who is also president of the LDP.
In July 2000, on the explicit invitation of Kim Jong-il - an unprecedented event - Putin paid an official visit to North Korea. "There will be less light in households due to less kerosene".
He also spoke over phone with German Chancellor Angela Merkel and South Korea President Moon Jae-In.
Wearing a pink Korean dress and flashing a wide smile, television presenter Ri Chun Hee delivered the news of Pyongyang's sixth nuclear test with her usual gusto.
Trump's call to Xi is part of his efforts to reach out to global leaders on the issue of North Korean threat. "The potential consequences of military action are too horrific", the Secretary General said. She pushed for the "strongest possible measures" against Pyongyang following its sixth and most powerful nuclear test.
A separate issue of South Koreans seeking compensation for forced labor during Japan's 1910-1945 colonial rule of the Korean Peninsula is another thorny issue.