The shares hit as high as $701.44 in morning trading Tuesday, 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.
(Copyright 2012 by The Associated Press. All Rights Reserved.)