In August, Trump told reporters that North Korean leader Kim Jong-un had "57 very powerful nuclear weapons" as he once again touted the pair's relationship.
North Korea on Sunday carried out a launch of a "suspected ballistic missile," the Japanese Prime Minister's office said, while South Korea's military reported that Pyongyang had fired an "unidentified projectile" into the East Sea.
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It comes after North Korea this week rejected a resolution by the UN nuclear watchdog against its nuclear programme.
A spokesperson for the country's Foreign Ministry said the International Atomic Energy Agency's resolution had "no effect on the DPRK's position as a nuclear weapons state."
In August, Trump told reporters that North Korean leader Kim Jong-un had "57 very powerful nuclear weapons" as he once again touted the pair's relationship.
"You know what, the fact that I get along with him, that's a good thing not a bad thing," Trump said, adding that Pyongyang's nuclear arsenal should "never" have been allowed to happen.
Trump announced at the time that he also intended to meet with Kim later this year, although he gave no further details on the plan - which would be their first meeting since Trump's first term in the White House.
On Friday, South Korean President Lee Jae Myung said he was "urging" Trump to maintain dialogue with Pyongyang, adding that Seoul was working to facilitate talks between the North and the US.
"I cannot say for certain how likely it is, but it is also clear that we must make every possible effort to turn that possibility into reality," he said of the potential for a meeting between US and North Korean officials.
However, hopes for an imminent meeting may have been doused slightly after Kim's powerful sister, Kim Yo Jong, criticised recent military drills in the Western Pacific, which she labelled a "US-led war rehearsal."
The US, South Korea and Japan wrapped up Exercise Freedom Edge 26, which US Pacific Command said advanced "trilateral readiness across the Indo-Pacific," on 11 September.
"Our will to defend our sovereignty will be expressed in clearer action and there will be never ever change in the course of intensifying the nuclear war deterrence," Kim Yo Jong added in a statement shared by North Korea's KCNA state news agency on Friday.