Apple Inc. has rejected Sony Corp.’s e-book reader app for the iPhone because it doesn’t give people the choice to buy books without leaving the app for a website.

The high-profile rejection shows Apple tightening control both over the way apps work and the way money flows through them.

Apple keeps a close eye on the iPhone and iPad programs that outside developers submit for distribution in the iTunes store. Sony’s Reader for iPhone app would have sent people to a website once they were ready to buy a book.

Apple’s insistence on an in-app purchase option can be seen as its way of ensuring that people using its gadgets get a familiar experience every time they make a purchase through an app. But such a move would prove less lucrative for companies such as Sony, because Apple takes a 30 percent cut of revenue from in-app purchases.

In the past, Apple has not enforced this rule across the board. Amazon.com Inc.’s Kindle e-book reading apps for iPhone and iPad don’t use in-app purchases, but rather send users to a website.

Sony protested what it calls a change in the way of enforcing the rules. “We opened a dialogue with Apple to see if we can come up with an equitable resolution, but reached an impasse at this time,” the company said.