Mr Trump also told the United Nations that if "forced to defend itself or its allies, we will have no choice but to totally destroy North Korea".
The Comprehensive Nuclear-Test-Ban Treaty Organization, through its executive secretary, tweeted Saturday that the activity was "unlikely man-made".
Chinese Foreign Minister Wang Yi said on Thursday (Sept 21) that negotiation remained the only solution on North Korea and warned its neighbours not to pursue their own nuclear weapons.
The United States Geological Survey was neutral in its assessment on the cause of the tremor, which it recorded as a 3.5 magnitude quake, saying in a statement that it could not "conclusively confirm at this time the nature (natural or human-made) of the event".
Pyongyang conducted its sixth and most powerful nuclear test on September 3, claiming it had tested a hydrogen bomb that could be loaded into an intercontinental ballistic missile.
All North Korea's nuclear tests registered as earthquakes of magnitude 4.3 or above.
"I strongly suspect they have the capability to do this", said James Acton, a nuclear expert at the Carnegie Endowment for International Peace. Since Kim came to power after the death of his father Kim Jong Il in 2011, he has ramped up nuclear and missile weapon tests.
North Korean leader Kim Jong Un has lashed out as world leaders have tightened the screws on his regime in Pyongyang over its nuclear programme and repeated missile tests.
North Korean Foreign Minister Ri Yong-ho, in NY for the U.N. General Assembly, said Thursday evening that his country could detonate a hydrogen bomb over the Pacific Ocean, but also told reporters, "We have no idea about what actions could be taken, as it will be ordered by leader Kim Jong Un". They also argue against doing anything that might hurt ordinary North Koreans.
Kim earlier this week called Mr Trump "deranged" and said he would "pay dearly" for his threats.
North Korea has said it intends to build a missile capable of striking all parts of the United States with a nuclear bomb.
Kim said Trump's "mentally deranged behaviour" and his threat to destroy North Korea "convinced me ... that the path I chose is correct and that is the one I have to follow to the last, " Kim said in a statement.
"But we're not in this alone", he added.
Trump told the United Nations on Tuesday the United States would "totally destroy" North Korea if it threatened the United States or its allies.
"It is a foolish misjudgment if Trump's gang thinks that America is safe because it's far away from the Korean Peninsula".
The Chinese Ministry of Commerce said in a written statement that it will restrict exports of refined petroleum products from October 1, and ban the export of condensate oil and liquefied natural gas immediately.
The UN Security Council voted on September 11 to limit fuel supplies and ban the North's textile exports.
"We resolutely condemned the nuclear missile adventures of Pyongyang in violation of Security Council resolutions, but military hysteria is not just an impasse, it's a disaster", Lavrov said in a speech at the UN General Assembly.