WASHINGTON — The Metropolitan Police Department said on Wednesday that it had opened an investigation into whether NBC and David Gregory, the host of “Meet the Press,” broke the law when Mr. Gregory displayed a high-capacity gun magazine during an interview on Sunday with the vice president of the National Rifle Association.

NBC had asked the police for permission to use a high-capacity magazine and “was informed that possession of a high-capacity magazine is not permissible, and their request was denied,” said Officer Araz Alali, a police spokesman.

“This matter is currently being investigated,” he said. “I can’t get into any other specifics of this investigation.”

A spokeswoman for NBC declined to comment.

According to a federal law enforcement official, an NBC employee contacted the Bureau of Alcohol, Tobacco, Firearms and Explosives on Friday to ask whether it would be legal for Mr. Gregory to show the magazine on television without the ammunition. The bureau, which does not enforce Washington’s gun laws, said it would be legal. That information, however, was incorrect, as it is illegal to have any empty magazine in Washington, the official said.