In fact, the specter of Mr. Clapper’s flying into the last stronghold of hard-line communist dictatorship may be the director’s best chance to revise a national image that was bruised when he was asked, in an open congressional hearing, whether intelligence officials collected data about ordinary Americans. “No sir,” he responded. “Not wittingly.”

Months later the revelations by Edward J. Snowden, the former National Security Agency contractor, made clear that, in the most charitable interpretation, Mr. Clapper had issued a misleading statement to protect classified programs; he later conceded in a letter that “my response was clearly erroneous.”

The administration issued almost no details of the trip to North Korea, saying communications from Pyongyang were so scant that they did not immediately know what had taken place in the discussion. It was also not clear whether Mr. Clapper had spoken directly with Mr. Kim or had seen other North Korean leaders; Mr. Kim disappeared from public view this summer with what now appears to have been a painful leg ailment.

Mr. Clapper rarely announces his schedule and can travel with little notice. But last week he canceled, at the last moment, a speech at the Council on Foreign Relations in New York. He left shortly after that on his trip to the North.

Image Kenneth Bae, left, and Matthew Todd Miller in September. Credit... Wong Maye-E/Associated Press

Sending high-level emissaries to the North is a long tradition; in Mr. Obama’s first term, former President Bill Clinton went to secure the release of two American journalists who had been seized on a trip along the Chinese border with the North. But Mr. Clinton’s trip led to no fundamental change in relations, which have been in a deep freeze since the North conducted a nuclear weapons test, its second, in May 2009, just months into Mr. Obama’s presidency. One of Mr. Obama’s top Asia aides, Jeffrey A. Bader, said then that the test made everyone in the White House “North Korea hawks.”

Mr. Obama has not attempted the kind of broad engagement that he has pursued so vigorously with Iran, responding to the North’s provocations by pursuing a policy of freezing the country out of the international economy, in hopes the regime will eventually implode.