"This is a real threat to the world, whether we want to talk about it or not. North Korea is a big world problem and it's a problem that we have to finally solve," he said. "People put blindfolds on for decades and now it's time to solve the problem."
US officials have told Reuters tougher sanctions could include an oil embargo, banning North Korea's airline, intercepting cargo ships and punishing Chinese banks and other foreign doing business with Pyongyang.
The State Department said US Secretary of State Rex Tillerson would chair a special ministerial meeting of the Security Council on North Korea on Friday to discuss ways to maximise the impact of existing sanctions and show "resolve to respond to further provocations with appropriate new measures".
Tillerson and US Secretary of Defense Jim Mattis, Director of National Intelligence Dan Coats and General Joseph Dunford, chairman of the Joint Chiefs of Staff, will also hold a rare briefing on North Korea at the White House on Wednesday for the entire US Senate, Senate aides said.
Administration officials routinely travel to Congress to address lawmakers but it is unusual for the entire 100-member Senate to go to such an event at the White House, and for those four top officials to be involved.
The White House said Trump and German Chancellor Angela Merkel discussed the "urgent security challenge" posed by North Korea in a phone call on Monday.
In an earlier phone conversation with Trump, Chinese President Xi Jinping called for all sides to exercise restraint, as Japan conducted exercises with a US aircraft carrier strike group headed for Korean waters.
Angered by the approach of the USS Carl Vinson carrier group, a defiant North Korea, which has carried out nuclear and missile tests in defiance of successive rounds of UN sanctions, said the deployment was "an extremely dangerous act by those who plan a nuclear war to invade".
"The United States should not run amok and should consider carefully any catastrophic consequence from its foolish military provocative act," Rodong Sinmun, the official newspaper of North Korea's ruling Workers' Party, said in a commentary.
Two Japanese destroyers have joined the US carrier group for exercises and South Korea said it was in talks about holding joint naval drills.
South Korean and US officials have feared for some time that a sixth North Korean nuclear test could be imminent and speculation has grown that this, or another missile test, could coincide with the 85th anniversary of the foundation of North Korea's army on Tuesday.
Trump has vowed to prevent North Korea from being able to hit the United States with a nuclear missile and has said all options are on the table, including a military strike, although officials say tougher sanctions are the preferred route.
China, North Korea's sole major ally, has been angered by its nuclear and missile programmes and its belligerence.
Xi told Trump China "hopes that all relevant sides exercise restraint, and avoid doing anything to worsen the tense situation", China's foreign ministry said in a statement.
It said the call was the latest manifestation of the close communication between the presidents, which was good for their countries and the world.
US ambassador to the United Nations Nikki Haley said Washington and the international community were maintaining pressure on North Korean leader Kim Jong Un but "not trying to pick a fight with him".
Asked whether a pre-emptive strike was under consideration, she told NBC's "Today" programme: "We are not going to do anything unless he gives us reason to do something."
"If you see him attack a military base, if you see some sort of intercontinental ballistic missile, then obviously we're going to do that. But right now, we're saying 'don't test, don't use nuclear missiles, don't try and do any more actions', and I think he's understanding that. And China's helping really put that pressure on him."
Trump also spoke by phone with Japanese Prime Minister Shinzo Abe.
"We agreed to strongly demand that North Korea, which is repeating its provocation, show restraint," Abe told reporters. "We will maintain close contact with the United States, keep a high level of vigilance and respond firmly."
Envoys on the North Korean nuclear issue from the United States, South Korea and Japan are due to meet in Tokyo on Tuesday.
The US government has not specified where the carrier strike group is but US Vice President Mike Pence said on Saturday it would arrive "within days".
Adding to the tension, North Korea detained a US citizen on Saturday as he attempted to leave the country.
(Reporting by Steve Holland in Washington and Ben Blanchard in Beijing; Additional reporting by Matt Spetalnick, Susan Heavey and David Brunnstrom in Washington, Takashi Umekawa and Linda Sieg in Tokyo, James Pearson in Seoul; and Philip Wen and Michael Martina in Beijing; Editing by Lisa Shumaker and James Dalgleish)