Trump said, "We know it kidnapped a sweet 13-year-old Japanese girl from a beach in her own country to enslave her as a language tutor for North Korea's spies".
It said Beijing "will never accept the "responsibility" imposed by the U.S".
The angry statement from Pyongyang's foreign ministry came as the crisis surrounding the reclusive state was set to dominate the annual United Nations gathering of world leaders.
In his debut address to the assembled world leaders Tuesday, Trump vowed to "totally destroy" North Korea if the U.S. was forced to defend its allies, saying that while the United States has "great strength and patience", its options could soon run out.
"Ramping up military hysteria in such conditions is senseless; it's a dead end", Russian President Vladimir Putin said earlier in September.
"Now is the time to apply pressure", Japanese Prime Minister Shinzo Abe, in New York for the General Assembly, told a gathering of investors at the New York Stock Exchange.
A U.S. official said that Trump would later Thursday make an announcement of further sanctions on North Korea.
Lavrov said Russia's position on the issue is "completely identical" to China's, the statement said.
Japan has taken a hard line on North Korea and has pushed for increased sanctions and pressure.
A pair of Air Force bombers and four stealth fighter jets conducted the live-fire training mission over the Korean Peninsula, the US military's Pacific Command reported.
Donald Trump Thinks North Korea Crisis Is Hillary Clinton's Fault, Because Huh?
Trump called the Iran deal one-sided and "an embarrassment to the United States". Still, the impasse is no closer to being resolved. Fears of a military confrontation are increasing.
US officials scrambled to stress diplomatic options remained open after Trump used his U.N. General Assembly speech on Tuesday to threaten to "totally destroy" nuclear-armed North Korea and blast Kim as a "rocket man" on a suicide mission.
South Korea officially played them down, while some politicians anxious that Trump's words signaled a loss of influence for Seoul.
The missile blasted off from near the Sunan International Airport north of Pyongyang, the North Korean capital, and flew about 2,300 miles, flying over northern Japan, the South Korean military said in a statement. Intelligence officials believe that the North's program has advanced to the point where it is no longer as reliant on outside suppliers, and that it may itself be making the potent fuel, known as UDMH. "The Punggye-ri nuclear test site remains ready for a (new) test", the ministry said.
Just two days ago, North Korea fired a ballistic missile over the northern Japanese island of Hokkaido, the latest in a series of missile tests defying the worldwide community.
China's Foreign Ministry, asked to respond to Trump's comments, said United Nations resolutions made clear the Korean peninsula issue should be resolved through political and diplomatic means.
The United States often sends such high-tech, powerful aircraft in a show of force in times of heightened animosities with North Korea.
Guam, a base for United States naval and air forces, is about 3400km from North Korea, a distance that an intermediate-range ballistic missile could reach.
"No one wants war, the president doesn't want war".
He added: "To prepare for an emergency, we would like to make every effort possible to protect the people's safety".
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