Pyongyang has launched a series of missiles this year, including a Hwasong-12 intermediate-range projectile this month.
Trump's tough talk came in a meeting with Prime Minister Shinzo Abe of Japan, which along with South Korea is most immediately threatened by North Korean belligerence.
But the isolated regime has also threatened to target places further afield such as the US West Coast, and Trump has called North Korea's young leader Kim Jong-Un a "madman with nuclear weapons".
"We will be discussing many things including of course North Korea which is very much on our minds," he said in the Sicilian town of Taormina as he held bilateral talks with Abe at the start of the two-day G7 summit.
"It's a big problem, it's a world problem.
"It will be solved, you can bet on that," he added, without giving further details.
North Korea carried out two atomic tests last year, and has accelerated its missile launch programme, despite tough UN sanctions aimed at denying Kim the hard currency needed to fund his weapons ambitions.
So far Washington has opted for sanctions and diplomatic pressure, while looking to China, the North's closest ally, to help rein in Pyongyang.
Earlier this month naval exercises were conducted in the Sea of Japan (East Sea) by the aircraft carrier USS Carl Vinson, with South Korean and Japanese aircraft also taking part.
Abe said he intended to use the G7 summit to underscore the danger posed by the unpredictable regime in North Korea.
"The issue of North Korea is a grave threat not only to East Asia but also to the world," he told reporters before leaving Tokyo, urging the G7 to act "resolutely".
Pyongyang's launches this year have included a Hwasong-12 intermediate-range missile this month which the North claimed was capable of carrying a "heavy" nuclear warhead, fuelling tensions with Washington.
The US is worried that if Kim is not stopped, other countries in the region including Japan and South Korea would be compelled to seek their own nuclear capability as a defence measure.
Washington says it is willing to enter into talks with North Korea if it halts its nuclear and missile tests, but it has also warned that military intervention is an option, sending fears of conflict spiralling.
In an April telephone conversation with Philippine President Rodrigo Duterte, Trump said "we can't let a madman with nuclear weapons let on the loose like that".
"We have a lot of firepower, more than he has, times 20 -- but we don't want to use it," the US leader said, according to a transcript of the conversation released by US media.
Trump also queried Duterte about whether he believed Kim was "stable or not stable". The controversial Philippine leader responded that their North Korean counterpart's "mind is not working and he might just go crazy one moment".
The United States has for weeks been negotiating a new Security Council sanctions resolution with China.
But Beijing, the North's main trade partner, has made clear that the push for diplomatic talks -- not imposing more sanctions -- is the priority.
North Korea has also been accused of being behind the ransomware epidemic that hit global computer networks earlier this month, crippling hundreds of thousands of computers.
Pyongyang has angrily dismissed these allegations.