“He has shown he does not have the tactical brain to lead the side,” Pietersen wrote in his column for The Daily Telegraph.
“Only politics are keeping Cook in a job because the England and Wales Cricket Board backed him so much that it would be yet another PR disaster if it sacked him now,” he said.
Cook, 29, has overseen seven defeats in the past nine England Test matches and failed to make a hundred in 27 innings.
The third of five tests against India starts at Southampton on Sunday with India leading the series 1-0.
Pietersen, who was axed by England in February following the team’s terrible winter tour to Australia, said: “Alastair Cook is enduring an experience I would not wish on my worst enemy, but he should do what is right for England and resign the captaincy.”
Pietersen said Cook should take advice from some of the ex-England players now working in the media.
“There are so many great cricket brains in the Sky studios,” he wrote. “Put that radio in your ear, listen to them on the balcony or in the dressing room and Mike Atherton, Nasser Hussain, (Shane) Warne or whoever could be saying something you didn’t know and could implement in the game.”
He suggests Ian Bell as a successor while Yorkshire’s Joe Root has the character to become captain but, at 23, is too young, he said.
Pietersen, England’s all-time leading run-scorer who hit 23 centuries in 104 Tests, was also critical of Cook’s technique and recommended he seek the assistance of Surrey head coach Graham Ford, to whom he turned during a poor run.
“He could have another 10 years left but his batting needs emergency help and he needs to speak to someone away from the England set-up,” he said.
“He should not stand there and let medium pacers bowl him half-volleys all day long and get him out. Someone of his size, strength, ability and with his eye should be hitting half-volleys for four all day.
“There is hope,” he added. “He is a popular guy so people will want to help him out and at 29 you do not lose everything.
“You take a couple of months out and find a new game. He then comes back and starts hitting medium pacers through the covers and half-volleys down the ground and suddenly opposition teams think, ‘Oh no he has cracked it’.
“Problem solved and Cook is now scoring runs for England again. But it will take help from elsewhere to solve this problem.” (Reuters)