"The era of strategic patience with the North Korean regime has failed," Trump said in a statement from the Rose Garden. "And, frankly, that patience is over."
The remarks were the latest sign that Trump is growing increasingly frustrated with the lack of progress in curbing North Korea's nuclear and ballistic missile programs, which top US officials have eyed with increasing concern in recent months.
The South Korean President's visit to the White House came after Trump approved a series of measures designed to ratchet up pressure on North Korea -- while also sending signals to China about the US' shrinking patience.
The Treasury Department on Thursday imposed new sanctions on a Chinese bank and several Chinese nationals while the State Department approved a $1 billion arms deal with Taiwan. Both moves appeared aimed at unsettling China, which the US has repeatedly urged to pressure North Korea into changing its behavior, with little success.
Trump on Friday warned that the US is facing "the threat of the reckless and brutal regime in North Korea" that "has no regard for the safety and security of its people or its neighbors" and vowed the US would continue to act to defend US interests and allies in the region.
Moon, who was elected on a platform of increased engagement with North Korea, also warned that "threats and provocations from the North will be met with a stern response" and vowed South Korea and the US will "strengthen" their joint deterrence capabilities.
But he also urged the North Korean regime "to promptly return to the negotiating table" to achieve a peaceful end to its nuclear program.
Beyond its ongoing nuclear and ballistic missile activity, the sense of alarm in the US has also grown after American student Otto Warmbier fell into a coma while in North Korean custody and died days after he was returned to the US.