"We are exploring options for a response to this series of provocations with our Security Council colleagues", the spokesman said.
Previously, the US itself prepared a plan of evacuation of its 230,000 citizens from the southern part of the Korean Peninsula.
The verbal blast comes as United States and Chinese diplomats at the United Nations are believed to be discussing how to impose stricter sanctions on North Korea should it conduct a new nuclear test.
Asked Wednesday about Kim's detention, the U.S. State Department said that it was aware of the report about a U.S. citizen being detained, but declined further comment "due to privacy considerations".
"One must clearly understand that the DPRK's line of access to nukes for the existence and development of the country can neither be changed nor shaken and that the DPRK will never beg for the maintenance of friendship with China, risking its nuclear program which is as precious as its own life, no matter how valuable the friendship is", it said.More news: Bulls' Rondo fined for attempting to trip Celtics' Crowder
North Korea's official news agency leapt into overdrive Wednesday, accusing Chinese politicians and journalists of fomenting trouble and outright "betrayal".
The Trump administration has recently increased its military strength in the region, sending a nuclear-powered aircraft carrier to Korean waters. The U.S. also activated its THAAD anti-missile defense system in South Korea this week at a former golf course.
The city of 600,000 people, just about 100 km (60 miles) from the border with North Korea, is home to thousands of North Koreans who mainly work on construction or do home renovations.
But ties have begun to fray in recent years, with China increasingly exasperated by the North's nuclear antics, fearful of a regional crisis.
He is now the third American being detained in North Korea.More news: Turkey's EU dream is over, for now, top official says
"If it would be appropriate for me to meet with him, I would absolutely, I would be honoured to do it", Trump told Bloomberg News.
The commentary late Wednesday added that Pyongyang had acted as a buffer between Beijing and Washington since the Korean War in the 1950s, "contributed to protecting peace and security of China" and that its ally should "thank the DPRK for it".
In a telephone call with his Philippine counterpart Rodrigo Duterte, Xi urged all sides to return to talks as soon as possible, Chinese state radio reported.
Russian Federation is also the source of foreign exchange for North Korea, mostly from Vladivostok. North Korea has also said that it would not abandon its missile and nuclear programs unless the usa ended its hostility toward Pyongyang. It called on the North to end its nuclear tests.
It added that the Swedish embassy in Pyongyang - which handles issues involving USA citizens as Washington has no diplomatic ties with the North - was "actively involved" in talks.More news: Declining Energy Trade Drives Canada's Record Deficit in 2016