There was no immediate reaction from China's Foreign Ministry, but the news was widely reported by Chinese state media outlets and on social media.
The United Nations agreed fresh sanctions - including the textiles and petroleum restrictions - in response.
The president has made it perfectly clear his mission was North Korea's "complete denuclearization".
"The quake has been analyzed to have occurred naturally", an agency official said.More news: Jai Lava Kusa Friday Box Office Collection
A limited amount, allowed under the United Nations resolution, would still be exported to North Korea.
But the ban on textiles - Pyongyang's second-biggest export - is expected to cost the country more than $700m (£530m) a year. "China and Russian Federation to have them also engaged with Pyongyang on this issue".
The 2018 Games are to be staged in Pyeongchang, just 80km from the demilitarised zone between North and South Korea, the world's most heavily armed border.
"It was $1.90 yesterday, today it is $2", a petrol station employee told the agency.
Treasury Secretary Steve Mnuchin said he spoke at length with the head of China's central bank but "I am not going to comment on confidential discussions".
North Korea's weakest nuclear test, its first one, conducted in 2006, generated a magnitude 4.3 quake.More news: Kingsman: The Golden Circle: hellaciously violent and a whole pile of fun
"I will surely and definitely tame the mentally deranged USA dotard with fire", Kim said in a statement filled with colorful insults that responded to Trump's own calling of the North Korean leader as "rocket man".
Moscow's foreign minister Sergei Lavrov has described the scrap as resembling a "kindergarten fight between children".
Mr Lavrov said a pause was needed, "to calm down the hotheads".
"I will make the man holding the prerogative of the supreme command in the USA pay dearly for his speech calling for totally destroying the DPRK". "I will surely and definitely tame the mentally deranged USA dotard with fire".More news: Two arrested in Banihal terror attack, snatched weapons recovered
"As stated by the respected Supreme Leader, our army and people, staking the dignity and honor of Juche Korea, will force the dotard to pay dearly for his reckless remarks and turn out in response to the call of the leader so as to surely and definitely tame the USA imperialist empire with fire and win the final victory in the standoff with it", the KCNA quoted one of the unnamed speakers as saying.