NEW YORK » Apple’s stock has reached $700 for the first time, setting a record for the company the day after it announced that orders for its iPhone 5 topped 2 million in the first 24 hours.

The shares hit as high as $701.44 in morning trading today, up a quarter of a percent from Monday’s close. It later fell.

The rally in its stock price puts its value at $656 billion, more than any public company has ever been worth, if one ignores inflation.

The Cupertino, Calif., company started taking orders for the iPhone 5 last week. Apple now says that while most orders will be delivered on Friday, demand for the iPhone 5 exceeds the initial supply. That means some of the devices will be delivered in October.