The incident was initially reported at about 2:20 p.m. about a half-mile east of Eagles Point, spokesman George Durgerian said.
The people and dog apparently went into a closed area of the park and ended up stuck down the cliffside, Durgerian said.
Park rangers and San Francisco firefighters responded and were working on rescuing the man, woman and dog by rope line as of 3:40 p.m., he said.
No injuries have been reported from the incident.
