LAGUNA BEACH, CALIFORNIA — Citing figures from partners Visa and Mastercard, Apple CEO Tim Cook says that his company's week-old digital payments service, Apple Pay, is already more successful than all other smartphone payment services combined.

"Visa and Mastercard. We talked to these guys today, and they told us that if you sum up everyone else that's in contact-less mobile payments at the point of sale, we're already number one," Cook said on Monday evening at the Wall Street Journal's WSJD conference in Laguna Beach, California. "We're more than the total of the other guys." According to Cook, users activated over 1 million credit cards on the service in its first 72 hours.

The company unveiled Apple Pay last month, alongside its wearable computer, the Apple Watch, and the service went live last week, with the arrival of the latest iPhones.

Many others have offered similar services, from PayPal to Google. But Apple is in a unique position to finally expand smartphone payments to a mainstream audience. With the iPhone, the company controls both the hardware and the software needed to operate a mobile payments service, and it has the clout to establish the necessary partnerships with credit card companies, banks, and merchants. At launch, Apple had established partnerships with all the major credit cards companies—American Express, MasterCard, and Visa—and it said that the service would be accepted at more than 220,000 merchants locations.

That said, we've already seen some push back from certain merchants. According to reports, drugstores chains CVS and Riteaid have blocked Apple Pay, apparently because they want to roll out a competing service, and Cook acknowledged that there are still difficulties ahead. "I think it's a skirmish," he said. "We have a lot more to go. We have a lot of merchants to sign up. We have a lot more banks to sign up. And we have the whole rest of the world. We are only in the U.S. right now."

Before Cook took the conference stage, Jack Ma, founder of China ecommerce giant Alibaba, said he was interested in establishing a partnership between Apple Pay and Alipay, the payments service spun out of Alibaba that he owns a majority stake in, and Cook indicated that he and Ma would be discussing such a thing in the coming week.

Update: This story has been updated with additional information from Tim Cook's Monday evening interview.