Despite the increased tension, the United States has not detected any change in North Korea's military posture reflecting an increased threat, the top USA military officer said on Tuesday.
A military option is not the preferred one, but Mr Trump added: "If we have to take it, we will".
Last month, Defence Industry Minister Christopher Pyne confirmed the Government was considering upgrading the Navy's new air warfare destroyers to include missile defence shields after "very irregular behaviour" by North Korea. His latest warning came in response to North Korea's threat a day earlier to shoot down approaching American bombers, even in worldwide air space.
Anthony Ruggiero, a senior fellow at the Foundation for Defense of Democracies, said the development "shows that China is not a reliable partner". There, Trump said the USA would "totally destroy" North Korea if necessary.
The US Treasury Department on Tuesday approved a new package of sanctions on eight North Korean banks and 26 financial representatives working in various countries. The war of words between the Kim Jong-un regime and Donald Trump administration has accelerated in recent weeks.
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"When the South has wartime operation control, the North will fear us more, and our armed forces will be trusted more", he said. "This action is also consistent with UN Security Council Resolutions", he announced.
North Korea has said it intends to build a missile capable of striking all parts of the United States with a nuclear bomb.
"By this stage, USA companies are generally not transacting directly with North Korea".
But Tong Zhao, a fellow at the Carnegie-Tsinghua Center for Global Policy in Beijing, said China didn't violate any United Nations sanctions with the August coal imports. The US, China and Russian Federation have also said they back the so-called Four Nos: No regime change, regime collapse, accelerated reunification and military deployment north of the 38th parallel.
North Korean Foreign Minister Ri Yong Ho said Mr Trump's Twitter comments, in which the USA leader said Mr Ri and leader Kim Jong Un "won't be around much longer" if they acted on their threats, amounted to a declaration of war and that Pyongyang had the right to take countermeasures.