LAGUNA BEACH, Calif.--Apple Inc. Chief Executive Tim Cook said more than one million credit cards were activated on the company's new Apple Pay service within 72 hours of its debut last week.

Speaking at the WSJD Live Global Technology Conference, Mr. Cook said the number of activations makes Apple Pay the largest mobile-payment offering.

Mr. Cook said reports of retailers such as Rite Aid Corp. and CVS Health Corp. not accepting Apple Pay at stores amounted to a skirmish. Neither company had officially joined Apple's network, but some customers last week found they could use Apple Pay in Rite Aid and CVS stores. The two retailers later disabled that functionality; it wasn't immediately clear why.

Rite Aid and CVS, along with Wal-Mart Stores Inc. and Best Buy Co., are part of a retailer-owned mobile-technology group called Merchant Customer Exchange, which will employ software that can be used on both iPhones and Android phones. The service is still in pilot mode and won't roll out nationally until next year.

Mr. Cook expressed confidence that Apple Pay will thrive in the long run.

"You are only relevant as a retailer or merchant if your customers love you," he said. "It's the first and only mobile payment system that's easy, private and secure."

Apple started its payment service on Oct. 20, allowing U.S. consumers to buy items at more than 220,000 stores or inside apps using the latest iPhones and a thumbprint.

Apple has signed up the six biggest credit-card issuers, accounting for roughly 83% of credit-card transactions in the U.S., with 500 financial institutions coming by early next year. It also has the three major credit-card networks: Visa Inc., MasterCard Inc. and American Express Co.

Despite the potential and growth of Apple Pay, Mr. Cook said the iPhone will probably comprise the majority of the company's revenue and profit for the next three to five years.

Asked about suggestions from investor Carl Icahn that Apple should repurchase more of its own shares, Mr. Cook said dryly, "Yes, we have some cash."

Apple reported holding roughly $155 billion in cash and investments at the end of September. Mr. Cook said Apple bought back $17 billion worth of stock during the September quarter, and $45 billion in the fiscal year through September.

Mr. Cook said share repurchases are a good thing, but secondary to reinvesting in Apple's business.

He also addressed recent criticism from law enforcement regarding Apple's decision to encrypt data on its iPhones when locked.

"I look at that and say if law enforcement wants something, they should go to the user and get it. It's not for me to do it," said Mr. Cook.

He added that it was better that the company didn't design its products "with the keys under the mat," because hackers could exploit the same opening.

Mr. Cook also made a thinly veiled criticism of Google Inc., saying that Apple wasn't checking what its users are searching, reading its users" email, or tracking the temperature in their homes or what they are buying.

"We're not Big Brother," said Mr. Cook. "We'll leave that to others."

An email sent to Google PR wasn't immediately answered.

Shira Ovide and Rolfe Winkler contributed to this article.

Write to Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com

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