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The agency said the seals became agitated when they spotted the man, who fled up a cliff face to escape the aggressive animals.
The man became stranded about three quarters of the way up the cliff and used his cellphone to call for help.
Coastguard crews from Dunbar, Berwick, North Berwick and Eyemouth responded alongside police and Eyemouth Royal National Lifeboat Institution.
The rescuers lowered a coastguard rescue officer from the top of the cliff, and the rescuer and angler were then lowered to a boat waiting below.
The man was not injured, but was treated for minor cold exposure, rescuers said.
"Anyone who encounters a seal or a colony of seals on the beach or coastline is advised to move away at the first sign of agitation," Senior Coastguard Operations Officer Jonathan Mustard said.
"Aggressive seals are not a common occurrence and in this case they may have been protecting or defending their natural habitat and their young. Remember to take a fully charged mobile when walking on the coast and call 999 and ask for the coastguard if you get into difficulty," he said.