It is hard to know which is worse: the latest claim that President Obama did not know that the National Security Agency was listening to the official and private telephones of some 35 world leaders, including German Chancellor Angela Merkel and Brazil’s President Dilma Rousseff, or the possibility that he did know and is now denying it.

Many people around the world will assume that our president is dodging the issue, an assumption that will swiftly erode respect for a man with more than three years left in our nation’s highest elective office.

But if administration officials are telling the truth, then we are left with the impression of a runaway spy agency and a clueless president.

According to several media outlets, high-ranking NSA officials said over the weekend that President Obama learned only this summer that the agency was listening to the telephones of world leaders.

One official told The Wall Street Journal that Mr. Obama immediately ordered the agency to stop its surveillance of Chancellor Merkel and some — but not all— of the other leaders on the NSA’s list.

According to those reports, the NSA, not the president, was responsible for the decision to initiate the surveillance. In the Journal story, the unnamed official said: “These decisions are made at NSA. The president does not sign off on this stuff.”

This is the first acknowledgement that some news stories about NSA surveillance of foreign leaders are accurate. A spokeswoman for NSA, however, said that a story in the German press accusing President Obama of personally authorizing the surveillance of the German Chancellor was false.

Friendly foreign governments are furious about the spying reports, which are doing major damage to U.S. foreign relations.

If the administration’s story that the president was unaware of the surveillance for more than four years is not challenged, the implications are as troubling as if he had authorized the spying disclosed by renegade NSA contractor Edward Snowden, now taking refuge from U.S. prosecution in Russia.

The story suggests that the president and his top staff were kept in the dark about essential details of the NSA’s operations. Since the president is ultimately responsible for the activities of the intelligence community, that suggests a shocking degree of irresponsibility in the people Mr. Obama chose as his top national security aides.

The story also suggests that the NSA operates without supervision and oversight, despite what Mr. Obama claims are well- designed constraints that protect Americans from its spying.

In its effort to deflect blame from the president to NSA, the White House has given Americans reason to be even more concerned about an apparent vacuum of national leadership.