Fans of Apple Inc.’s (AAPL) iPhone had difficulty pre-ordering the iPhone 4 from AT&T Inc.’s (T) Web site on Tuesday.

The wireless carrier’s site was supposed to begin accepting pre-orders for the phone, which goes on sale June 24, but could not handle demand. The company said today marked the site’s busiest day in history for sales online, according to a report by the Wall Street Journal.

The technical difficulties created by the rush of customers caused order-processing difficulty, as well as revealing the personal information of some AT&T subscribers to others by confusing user accounts, the paper said.

AT&T has had other security problems lately, including a confirmed glitch which allowed computer hackers to access the email addresses of thousands of Apple iPad owners, earlier this month.

The company said iPhone 4 preorders that would be delivered on June 24 were sold out and that future orders will not arrive until June 25 or later, according to the Journal’s report. The new phones will still be available in stores on June 24.

Shares of Apple rose $5.41 or 2.13% on Tuesday, closing at $259.69 a share. AT&T shares gained 37 cents or 1.47% during the trading session Tuesday, closing at $25.54.