AT&T ( T) said Friday that the privacy rights group that sued AT&T over the company's handling of customer information is "suing the wrong party."

The Electronic Frontier Foundation has filed a civil suit that aims to limit phone companies' sharing of customer data with the government. The suit was filed after news reports said AT&T, BellSouth ( BLS) and Verizon ( VZ) handed over millions of customer records to the National Security Agency to assist the feds' antiterror efforts.

The case is being heard by U.S. District Judge Vaughn Walker in San Francisco. He conducted hearings Friday but didn't issue a ruling, AT&T spokesman Walt Sharp says.

In a press statement late Friday, AT&T says the plaintiff's "real dispute is with the government."

"We asked the judge to dismiss this lawsuit based on a series of statutory and common law immunities that exempt corporations from civil lawsuits which contain claims or allegations that the companies cooperated with government or law enforcement agencies regarding national security matters," AT&T says. "These provisions make it clear that, even if AT&T were acting as alleged, AT&T cannot be sued, as the real dispute is with the government. Congress gave companies this immunity to ensure their cooperation with critical national security issues."

AT&T also says it hasn't broken the law in any of its dealings with the government. "We prize the trust our customers place in us and, in all instances, AT&T obeys the law," the company says.

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