“We have said to the North Koreans that there’s a path to better relations,” Mr. Obama said in an interview with MSNBC. “We just want to make sure the government of North Korea is operating within the basic rules of the international community that they know is expected of them.”  Mr. Obama’s message, repeated by Secretary of State Hillary Rodham Clinton, illustrated the determination of the White House not to allow Mr. Kim to turn Mr. Clinton’s visit to his advantage in talks with the United States and other countries.  Still, the events of the past two weeks show that relations between the United States and the North are, if nothing else, rich in diplomatic theater, with a new American administration working to find the right tone and strategy for dealing with a country that has confounded multiple presidents, including Mr. Clinton.  Officials said the administration’s restatement of its policy did not mean that it was blind to the opportunities that could flow out of the mission’s happy outcome.  “How this impacts the psychology of the North Koreans, no one can tell,” said a senior administration official, who spoke on the condition of anonymity because of the delicacy of the issue.  The White House began to debrief Mr. Clinton later on Wednesday, after he had short phone conversations with Mr. Obama and Mrs. Clinton, who is traveling in Africa. After delivering Ms. Ling and Ms. Lee to their families at an airport in Burbank, Calif., Mr. Clinton flew to his home in Chappaqua, N.Y.  Among other issues, administration officials said, there is no established protocol for a face-to-face debriefing of a busy former president about intelligence and diplomatic matters. Do you summon him to the White House, or do you send a delegation to visit him?  Mr. Clinton has not spoken publicly about the trip, which was cloaked in secrecy until just before he arrived in North Korea.  He flew across the Pacific and back on a Boeing 737 that belongs to Steve Bing, a film producer and friend of the former president. Mr. Bing has been a major donor to Democratic candidates.  For all the talk of the North’s isolation, the United States and North Korea hold regular back-channel talks through North Korea’s United Nations mission. The so-called New York connection laid the groundwork for Mr. Clinton’s visit and will probably play a part in what comes next.  The release of the journalists could break an impasse between the United States and North Korea because, officials and outside experts said, there was virtually no prospect of reviving nuclear negotiations as long as the women appeared to be headed to a North Korean prison camp.  At the same time, Mr. Kim is likely to expect some kind of payback for the pardons, political analysts said.  How the United States responds to Mr. Kim’s expectations may determine whether Mr. Clinton’s visit leads to a genuine opening between the countries.  “They’re going to expect us to take our foot off the pedal,” said Victor Cha, who negotiated with North Korea in the Bush administration. “If China calls and says North Korea is willing to come back to six-party talks in Beijing if we relax the sanctions, this becomes a tough call.”  In a sign of the administration’s sensitivity, a senior official said the United States had briefed officials at the highest levels of the Chinese and Russian governments last weekend about the nature of Mr. Clinton’s mission, to reassure them that the White House did not intend the visit to lead to bilateral talks with North Korea.  One American official noted that Mr. Clinton, in his talks with Mr. Kim, broached the issue of Japanese and South Koreans abducted by North Korea — politically emotive matters for those countries, in their dealings with the North.  Some of the administration’s calculations will be influenced by Mr. Clinton’s observations about Mr. Kim’s health and mood. He suffered a stroke last year, and his diminished health led to speculation that the North was caught up in a struggle to succeed him.  American officials are also eagerly interviewing David Straub, a former director of the State Department’s Korea desk, who accompanied Mr. Clinton. Mr. Straub speaks Korean and took part in back-channel communications with North Koreans when he was in the government.  As the administration deliberates over North Korea, there are reports that the North is suspected of spreading its technology. The Sydney Morning Herald in Australia reported last week that Myanmar was building a nuclear reactor and plutonium extraction plant, with help from North Korea.  The acting State Department spokesman, Robert A. Wood, said Tuesday, “We’re obviously looking into these types of reports.” Mrs. Clinton said recently that there was concern about possible transfers of nuclear technology from North Korea to Myanmar.  Peter Baker contributed reporting from Washington, and Jeffrey Gettleman from Nairobi, Kenya.  A version of this article appears in print on , on Page A1 of the New York edition with the headline: U.S. Reminds North Korea: Work Remains. Order Reprints| Today's Paper|Subscribe
After former President Bill Clinton won the freedom of two American journalists, officials were busily calculating whether the psychology in Pyongyang had changed.