"It's a big problem, it's a world problem," he said in the Sicilian town of Taormina, just weeks after he called North Korea leader Kim Jong-Un a "madman with nuclear weapons."
The issue of North Korea, whose missile and nuclear tests have its neighbours and the wider world concerned, will be discussed in joint meetings with the other six heads of leading industrialised countries, Trump said.
"It will be solved, you can bet on that," he said before going into closed-door talks with Abe, without giving further details.
Abe intended to use the summit to underscore the danger posed by the unpredictable regime in North Korea following its recent series of missile tests.
"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 has launched a series of missiles this year, including a Hwasong-12 intermediate-range projectile this month which the North claimed was capable of carrying a "heavy" nuclear warhead, fuelling tensions with Washington.
It carried out two atomic tests last year, insisting it needs nuclear weapons to defend itself against the threat of invasion.
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.
North Korea lashes out at US
'A lot of firepower'
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 was 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.
Bishop: 'nuclear North Korea is a threat'
Trump also queried Duterte about whether he believed Kim was "stable or not stable." The 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 North Korea's ally 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 computer and demanding payment in Bitcoin to return control to users.
Pyongyang has angrily dismissed these allegations.
