Trump alluded to the use of force to reporters in London, where he is attending a meeting of North Atlantic Treaty Organization leaders, according to news reports.
However, Trump also said he continues to have a good personal relationship with North Korean leader Kim Jong-un and hopes he will abide by his commitment to dismantle his country's nuclear weapons program.
"Now we have the most powerful military we have ever had and we are by far the most powerful country in the world, and hopefully we do not have to use it," the US president was quoted as saying in the meeting with journalists.
"But if we do, we will use it. If we have to, we will do it," he said.
Hours earlier, the North's Vice Foreign Minister Ri Thae-song issued a statement urging the US to do its part to salvage the negotiations that have stalled since a second summit between Trump and Kim in February ended without a deal.
"The DPRK has done its utmost with maximum perseverance not to backtrack from the important steps it has taken on its own initiative," Ri said, referring to North Korea by its official name, the Democratic People's Republic of Korea.
"What is left to be done now is the US option and it is entirely up to the US what Christmas gift it will select to get," he said, in an apparent warning that unless the US comes up with a new offer before the end of the year, Pyongyang could restart nuclear weapons and long-range missile tests.
At a meeting with NATO Secretary General Jens Stoltenberg, Trump appeared to refer to North Korea's recent weapons tests, including the launch of two short-range projectiles from a super-large multiple rocket launcher last week.
"Likes sending rockets up, doesn't he? That's why I call him rocket man," Trump said, referring to Kim, according to news reports. "We have a very good relationship and we'll see what happens. It may work or not." (Yonhap)