Special master Richard Levie of the Justice Department has ruled that Sprint must give it, and by extension, AT&T, additional documents that relate to the effects of the iPhone on Sprint’s market share, reports Reuters.

The information is in addition to initial cache of documents already ponied up by Sprint in its cooperation with the DoJ’s efforts to block the $39B acquisition of T-Mobile by AT&T.

Sprint recently gained the ability to sell Apple’s iPhone 4 and iPhone 4S model, something it had not had before last month. This addition, which was made after the Justice Department filed its lawsuit to stop the acquisition.

“AT&T is entitled to discover what effect the iPhone and other events of the past few months have had on Sprint’s relevant market share, a part of the government’s …. case,” said Levie in the order to Sprint.

AT&T had apparently asked Sprint for documents that showed its negotiation with device makers, its research into the competitive nature of T-Mobile and its plans to target T-Mobile customers.

Sprint is estimated to be giving AT&T about 440,000 pages of documents. Sprint hates this idea because it has filed its own case against AT&T to stop the merger, a case that has not yet begun to get underway.

Sprint’s Dan Hesse has been quoted as saying that the iPhone is the “number one reason” that customers had been switching away from the network. This could be why Sprint was willing to pony up such a huge buy-in for the rights to carry the iPhone. Sprint reportedly pays a premium for every iPhone it sells, speaking to the device’s importance to its business.

Sprint reported it’s best retail sales day ever on the iPhone’s launch day, stating:

Sprint today reported its best ever day of sales in retail, web and telesales for a device family in Sprint history with the launch of iPhone 4S and iPhone 4. We reached this milestone at approximately noon CT/1pm ET. The response to this device by current and new customers has surpassed our expectations and validates our customers’ desire for a truly unlimited data pricing plan.

If the effects of the iPhone can be shown to have materially improved Sprint’s market share compared to AT&T, it is likely that it will be harder for the DoJ to oppose the effective merger of the second and fourth biggest wireless providers in the US.

Any gains that Sprint made over the launch of the iPhone could have been offset, however, as AT&T also reported a record number of iPhone activations on day 1 of the iPhone 4S launch.