The administration said in a statement on its website that the quake, which occurred around 0830 GMT, was recorded a depth of zero kilometres.
The U.N. sanctions were a response to North Korea's sixth nuclear test, which experts said was its biggest by far, earlier this month.
China's official Xinhua news agency said the epicentre was roughly at the same place as a similar shallow quake on September 3, which turned out to be caused by North Korea's sixth and largest nuclear test.
"As far as I know, what you mentioned now is not consistent with facts", Chinese Foreign Ministry spokesman, Lu Kang told reporters here, when asked about Trump remarks.
In response to North Korea's recurring nuclear and missile tests, the council has told its member countries to ban most activity overseas by the banks of that country.
Xinhau, China's official news agency, said the country's seismic service registered a 3.4 magnitude event that it originally viewed as "likely caused" by an "explosion".
Satellite photos of the area after the Sept 3 quake showed numerous landslides apparently caused by the massive blast, which North Korea said was a hydrogen bomb.
China has repeatedly called for peace talks, suggesting that Pyongyang halt its nuclear activities in return for the United States suspending military drills in the region. She said the analysis of seismic waves and the lack of sound waves clearly showed that the quake wasn't caused by an artificial explosion.
Moon may have been making his own personal appeal to Trump by quoting former U.S. President Ronald Reagan, one of Trump's heroes.
Tensions have continued to rise around the Korean Peninsula since Pyongyang carried out its sixth nuclear test, prompting a new round of United Nations sanctions. It will also ban imports of textiles from North Korea.
"The new sanctions set a cap on crude and refined oil exports to North Korea at 8.5 million barrels per year, which represents a 30 percent reduction, according to USA officials".
On Thursday Trump announced new USA sanctions that he said allows the targeting of companies and institutions that finance and facilitate trade with North Korea.
Saturday's detection comes at a time of rising tensions between the United States and North Korea, with North Korean dictator Kim Jong Un and President Donald Trump engaging in an escalating war of words.
The US treasury has been authorised to target firms and financial institutions conducting business with North Korea.