The bombers were joined by U.S. Air Force F-15C Eagle fighter escorts from Okinawa, Japan.
But in a new stage for such show of force operations, the Pentagon stressed this was the furthest north of the Demilitarized Zone (DMZ) between the two Koreas that any United States fighter or bomber has flown off North Korea's coast in this century.
North Korea's Foreign Minister said on Saturday that United States President Donald Trump's vow to "totally destroy" the country if necessary had made "our rockets' visit to the entire U.S. mainland all the more inevitable". On Thursday, Trump signed an executive order giving the Treasury Department more authority to cut off trade that helps finance North Korea's weapons and nuclear programs.
White says "we are prepared to use the full range of military capabilities to defend the USA homeland and our allies".
Ri on Friday said North Korea may test a hydrogen bomb in the Pacific Ocean, making those remarks after Trump inflamed tensions in his debut speech before the UN.
This flight of strength comes after a week of high tension, as President Trump called Kim Jong-un a "madman" a "rocketman" along with saying he is a "mentally deranged dotard".
Mr Ri's highly anticipated speech to the General Assembly's annual ministerial meeting fuelled the fiery rhetoric between the USA president and North Korea's young leader.
Scott Snyder, director of the programme on US-Korea policy of the Council on Foreign Relations, said Washington's latest move was aimed at putting further pressure on Pyongyang.
At the UN, North Korea's foreign minister said US President Donald Trump was on a "suicide mission".
U.S. Pacific Command would not be more specific about many years it had been since U.S. bombers and fighters had flown that far north of the DMZ, but a spokesman, Navy Cmdr.
"This event occurred in the area of the previous North Korean Nuclear tests", the United States Geological Survey said on its web site.
Seismic activity Saturday in North Korea, meanwhile, sparked fears that Pyongyang may have conducted yet another nuclear test, but experts said the small quake was probably due to natural causes.
On Thursday Trump announced new U.S. sanctions that he said allows the targeting of companies and institutions that finance and facilitate trade with North Korea.
His foreign minister has now said that Mr Trump is trying to convert the United Nations into a "gangsters nest" where "bloodshed is order of the day".
Calling the resolutions unjustified, Ri said that Pyongyang was left with no other choice but to respond with the "nuclear hammer of justice".