Speaking at a press conference after meeting the leader of Spain, Trump said all nations must act now for the de-nuclearization of North Korea.
"We are totally prepared for the second option, not a preferred option," Trump said at a White House news conference. "But if we take that option, it will be devastating, I can tell you that, devastating for North Korea. That's called the military option. If we have to take it, we will," he said.
Trump also repeated the praise he offered last week for China's reported breaking off of banking relations with North Korea.
There has been no official confirmation from China of such a step. China is North Korea's most important trading partner.
Trump's comments came after he ignored pleas to tone down anti-Pyongyang rhetoric, accusing the regime of having tortured a captive U.S. student "beyond belief."
The U.S. also imposed sanctions on eight North Korean banks and 26 executives on the same day, ratcheting up pressure on the country amid increasingly bellicose exchanges with Pyongyang over its nuclear program.
"This further advances our strategy to fully isolate North Korea in order to achieve our broader objectives of a peaceful and denuclearized Korean peninsula," U.S .Treasury Secretary Steven Mnuchin said in a statement.
Tuesday's announcement compounded economic sanctions which the United Nations unanimously imposed on North Korea after it carried out its latest nuclear weapons test early this month.
The new sanctions target North Koreans working as representatives of North Korean banks in China, Russia, Libya and the United Arab Emirates.
All property and interest of the designated companies and individuals in the U.S. are blocked by the sanctions, effectively freezing them out of much of the global financial system.
The U.S. targeted North Korea's Foreign Trade Bank and the Central Bank of the Democratic People's Republic of Korea as North Korean government agencies.
The Treasury's Office of Foreign Assets Control, which overseas U.S. sanctions programs, said the Foreign Trade Bank had carried out transactions on behalf of North Korea's weapons development program.
General Joe Dunford, chairman of the U.S. joint chiefs of staff, testified before lawmakers on Tuesday that for the time being the confrontation with North Korea was more political than military.