"Today, I am announcing a new executive order that significantly expands our authorities to target individuals, companies, financial institutions that finance and facilitate trade with North Korea," Trump stated before a working lunch with South Korean President Moon Jae-in and Japanese Prime Minister Shinzo Abe.
The sanctions target Pyongyang's information technology, manufacturing industries, as well as fishing and textiles.
Trump said the executive order gives the US Treasury Department discretion to impose punitive measures against any foreign bank that knowingly conducts transactions with North Korea.
Trump emphasized that any tolerance for Kim Jon-un's destabilizing activities should now end and called on the international community to aim for complete denuclearization of North Korea.
But he said "Why not?" responding to a question on whether dialogue with Pyongyang was still possible.
Tensions over North Korea's nuclear and missile programs have escalated in recent months as Pyongyang has test-launched a number of projectiles which flew over Japan and triggered global criticism. On Monday, the US president said Washington would "have no choice than to totally destroy North Korea" if immediate threats emerge.
Earlier, as a response to the potential use of nuclear weapons, the United States sent a strike group led by US aircraft carrier Carl Vinson to the Korean Peninsula, where it held exercises with the South Korean navy.
US media reported in mid-April that US President Donald Trump might order a strike against North Korea in light of its military activities. North Korean top officials said the country was ready for nuclear attacks in the event of possible US military aggression.