King intends to return to Washington from Tokyo on Saturday.
Bae's family expressed disappointment but said they were holding on to faith that North Korean and U.S. diplomats would resume talks soon.
"We have sought clarification from the DPRK about its decision and have made every effort so that Ambassador King's trip could continue as planned or take place at a later date," Harf said in a statement, referring to the country's formal title of the Democratic People's Republic of Korea.
"We remain gravely concerned about Mr. Bae's health and we continue to urge the DPRK authorities to grant Mr. Bae special amnesty and immediate release on humanitarian grounds," Harf said.
The North Korean diplomatic mission at the United Nations in New York declined to comment Friday.
In a sign that all was not well, North Korea abruptly took a stronger tone Thursday in its criticism of U.S.-South Korean military drills that began Aug. 19 and were concluded Friday.
Pyongyang had initially responded to those computer-simulated drills with milder-than-usual language, which was seen as a sign of its interest in keeping up diplomacy. The regime of leader Kim Jong Un has also moved in recent weeks to improve relations with South Korea, a staunch U.S. ally.
"The trend for reconciliation and unity has faced a serious challenge due to the reckless nuclear war moves and confrontational racket against the DPRK being kicked up by the U.S. and the South Korean warmongers," the North's National Peace Committee of Korea said in Pyongyang's characteristic, combative style.
In the statement carried by the state-run news agency, the commission accused the U.S. of flying nuclear strategic bombers above South Korea this week in an attack drill.
Former State Department official Evans Revere, who has negotiated with North Korea in the past over the fate of Americans detained there, said that the stronger reaction to the military exercise, coupled with the rebuff over King's visit, could be an attempt by Pyongyang to get under Washington's skin.
But he said that was unlikely to lead to the kind of dramatic escalation in tensions seen earlier in the year, and it would be interesting to see whether North Korea would reschedule the trip in the next couple of weeks.
Analysts say North Korea has previously used detained Americans as bargaining chips in its standoff with the U.S. over its nuclear and missile programs. Multination aid-for-disarmament talks have been on hold since 2009, and efforts by Washington to negotiate a freeze in the North's nuclear program in exchange for food aid collapsed 18 months ago.
Bae is at least the sixth American detained in North Korea since 2009. The others were eventually allowed to leave without serving their terms, with some releases coming after prominent Americans, including former Presidents Bill Clinton and Jimmy Carter, visited North Korea.
Bae was arrested last November and accused of committing "hostile acts" against North Korea. He suffers from multiple health problems.
On Wednesday in Tokyo, King had cautioned that Washington had received no guarantees from Pyongyang that Bae would be freed.
"We hold on to faith that DPRK and US diplomats will resume talks soon, ultimately leading to my brother being released," Bae's sister Terri Chung, who lives in Edmunds, near Seattle, said in a statement.
"It has been 301 days since Kenneth has been detained. With every day, we continue to pray. We appreciate the work that the State Department and the Obama administration have been doing and have pledged to do for Kenneth's release. We miss Kenneth and remain concerned about his health," the statement said.
Rep. Rick Larsen, who represents the Washington state district where Bae is from, said the North Koreans "gain nothing from this course reversal. It is time to let Kenneth come home to his family and get the medical attention he needs."
The last American to be detained by North Korea and then freed was Eddie Jun from California. The Korean-American was arrested for alleged unauthorized missionary work during several business trips to the country. He was brought back to the U.S. when King last visited Pyongyang in May 2011.
In August 2010, a State Department mission to free another detained American, Aijalon Gomes, ran into problems. A U.S. consular team was allowed to meet Gomes in Pyongyang but was not allowed to bring him home. He had been sentenced to eight years of hard labor for crossing into North Korea from China.
Two weeks later, former President Carter visited, and Gomes was released.
___
Associated Press writers Gene Johnson in Seattle and Alexandra Olson at the United Nations contributed to this report.
