Secret Service agents yesterday intercepted and disarmed a letter-bomb addressed to President Reagan and later in the day arrested a Washington man who climbed over the White House fence, officials said.

Jack Warner, assistant to the director of the Secret Service, said that the parcel, a 6-by-9-inch manila envelope, was postmarked San Juan, Puerto Rico. Warner described the explosive device the envelope contained as "rather amateurish," and said it would have caused "minimal, if any" damage if it had exploded.

Warner said the device was discovered at around 1:30 p.m. in the White House mail room when the envelope, like all incoming mail, was run through an X-ray machine. A Secret Service bomb disposal expert was called to defuse the device. Warner said the device could have caused some injury to a person opening the envelope, but added that the device was assembled so crudely that it might not have gone off at all.

Warner declined to release further details of the nature of the explosive device. He said the envelope contained no message and is being examined for evidence.

Meanwhile, a Secret Service spokeswoman identified the man who climbed the fence as William Persons, 23, of Washington. He was taken into custody as he began running toward the main doors of the White House. He was not armed, the spokeswoman said.