WASHINGTON (CNN) -- House Democratic leaders unveiled legislation Tuesday to update the nation's wiretapping program, rejecting a Senate-passed version of the bill that would give telecommunications companies legal immunity for agreeing to participate in the program after the 9/11 terrorist attacks.

President Bush secretly instituted the National Security Agency's domestic spying program after 9/11.

President Bush and House Republicans have insisted that the House pass the Senate version of the Foreign Intelligence Surveillance Act (FISA) bill.

Instead, top Democrats -- including House Majority Leader Steny Hoyer, House Intelligence Chairman Silvestre Reyes and Judiciary Chairman John Conyers -- proposed that lawsuits against the phone companies could move forward through U.S. district courts.

The government has effectively frozen all litigation by invoking the "state secrets" doctrine, arguing that documents detailing the phone companies' activities are classified.

Under the proposed legislation, the companies would be able to argue their cases in court and present classified evidence to a judge during a closed proceeding without the presence of the plaintiffs.

"We are not going to cave in to a retroactive immunity situation," Conyers said.

He argued that "there's no law school example in our memory that gives retroactive immunity for something you don't know what you are giving it for. It just doesn't work in the real world, or on the Hill either."

Texas Rep. Lamar Smith, the top Republican on the House Judiciary Committee, said that without immunity for telephone companies, the Democrats' surveillance bill would be "dead on arrival."

"Today's proposal is further evidence that House Democrats are not only out of touch with the needs of the American people, but also with Senate Democrats, the White House and our intelligence community," he said in a written statement. "Their careless disregard for the concerns of our intelligence community simply proves the point that Democrats are weak on national security."

A joint statement from the Department of Justice and the office of the director of national intelligence said that based on initial reports, "We are concerned that the proposal would not provide the intelligence community the critical tools needed to protect the country."

The statement also restates the administration's position that immunity protection is needed so the program can continue.

"Exposing the private sector to continued litigation for assisting in efforts to defend the country understandably makes the private sector much more reluctant to cooperate. Without their cooperation, our efforts to protect the country cannot succeed," it said.

Hoyer said the proposal sets up a new process for civil lawsuits, similar to one used in criminal cases, which "provides for the use of such secret documents in secret, not to be exposed, in secret by the courts as they do on a number occasions so that they can properly make their cases."

Conyers said there would be "no hammer" forcing judges to hear the cases with the process, but he said the proposal "takes it out of FISA, takes it out of Congress, puts it in the court system and ... the telecoms have their day in court."

Facing a certain veto from Bush, Conyers said, "This is our best way to resolve this matter, notwithstanding the president's threat. This is a reasonable, intelligent way to proceed without jeopardizing our responsibilities to fight terrorism."

The House version provides stronger court oversight of government surveillance than the Senate bill. It also adds a bipartisan commission modeled on the 9/11 commission to investigate the administration's warrantless wiretapping program. The commission would have subpoena power and would report back to Congress in one year.

Hoyer said the House will vote on the bill Thursday.

The Democrats' chief vote counter, Rep. James Clyburn of South Carolina, said he is confident the bill will pass the House.

But the measure is unlikely to get through the Senate.

Republicans object to any changes to the Senate bill, and the top Democrat on the Intelligence Committee, Jay Rockefeller, of West Virginia, released a statement saying the House bill is a "step in the right direction. But considerable work remains." E-mail to a friend

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