Apple's new contactless payment system on the iPhone 6 saw 1 million activations in its first three days of use, pointing to an initially enthusiastic response from Apple users.

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"In the first 72 hours, we've gone over the 1 million mark on activations on cards," Apple CEO Tim Cook said during an on-stage interview late Monday at The Wall Street Journal's technology conference in Laguna Beach, California.

"Visa and Mastercard have told us, if you sum up everyone else that's in the contactless mobile payment at the point of sale, we're already number one," he said. "Not just number one, but we're more than the total of all the other guys. And we've only been at it a week."

Cook said he uses it himself at his local Whole Foods supermarket.

Apple Pay was released on October 20 and allows users to make tap-and-go payments from their smartphones at retailer terminals equipped with wireless NFC (near-field communication) readers, of which there are over 200,000 in the U.S.

At launch, Apple Pay is being offered to users in the U.S. with an iPhone 6 and U.S. credit or debit card. Apple plans to launch it overseas in 2015.

"We've got a lot more to go," said Cook. "We have a lot more merchants to sign up, we've got a lot more banks to sign up and we've got the whole rest of the world."

While consumers appear to be enthusiastic about Apple Pay, some major retailers are not. After initially accepting the payment method, drug store chains Rite Aid and CVS have both started blocking NFC payment systems including Apple Pay and Google Wallet.

The two companies are part of a consortium of retailers attempting to launch their own phone-based payment system. Called CurrentC, the technology relies on a barcode that is displayed on the phone's screen and scanned at a payment terminal. It is expected to launch in 2015.

Cook called the issue a "skirmish."

Over time, Cook said, retailers will eventually have to do what shoppers want.

Martyn Williams covers mobile telecoms, Silicon Valley and general technology breaking news for The IDG News Service. Follow Martyn on Twitter at @martyn_williams. Martyn's e-mail address is [email protected]