Surprising fellow Judiciary Committee colleagues, Sen. Arlen Specter announced a deal Thursday on National Security Agency surveillance to let a court that handles foreign intelligence matters determine whether a key eavesdropping program is constitutional.

The newly-worded bill would give President Bush the option of submitting the eavesdropping program for review to the same court that approves warrants under the Foreign Intelligence Surveillance Act. Specter said he obtained the president's pledge that he will seek such a ruling.

"The president will submit the terrorist surveillance program to the Foreign Intelligence Surveillance Court," Specter said. "Understandably, the president does not want to institutionally commit future presidents, but the president has made the commitment."

The so-called terrorist surveillance program, begun by executive order after the Sept. 11, 2001, terror attacks, remains classified despite press reports last December that revealed its existence.

The program seeks to monitor phone calls involving one participant within the United States and one outside the country who is suspected of having terrorist links. The 1978 Foreign Intelligence Surveillance Act requires a warrant for anyone to wiretap phone calls within the United States, but the administration said it is within legal boundaries to monitor international calls whether or not they involved one party on U.S. soil.

Speaking during a Senate Judiciary Committee hearing, Chairman Specter said the negotiations had begun in earnest between him, his staff and members of the administration in June and the final touches on the proposed bill ended Wednesday evening. He said the president's agreement to the bill hinges on the condition that any changes are "satisfactory" to him, although Congress has some latitude to make changes.

The bill does not request individual warrants, but would allow the court to look at the program in a broad form so that a wiretap applies to a person who is roving rather than at a fixed number, Specter said. The bill also would extend the length of time that officials can request a warrant in a domestic wiretap case from three to seven days.

"There has to be judicial review before you can wiretap. That's been the tradition. Now the president said he had Article II power to do without that, and the president does have expansive Article II power, but not a blank check," Specter said of presidential authority outlined in the U.S. Constitution.

Specter clarified that the bill would narrow what amounts to foreign or domestic phone calls to exclude phone calls and e-mails that merely pass through the United States.

"A call from France to Jordan passing through a New York terminal would not be subject to FISA," he said.

As much as 90 percent of the world's e-mail goes through the United States so that would make it far easier to track terrorist communications.

White House spokeswoman Dana Perino said the four main points in the new legislation are significant: The bill would recognize the president's constitutional authority to collect intelligence on foreign powers; it would give the attorney general new tools to consolidate a number of lawsuits challenging the program; it would give the president the option to send challenges to the FISA court; and it would generally modernize FISA.

"It modernizes [FISA] to meet the threat we face from an enemy who kills with abandon," Perino said.

"There are aspects here which we think are very good," Attorney General Alberto Gonzales said of the bill, talking to reporters Thursday.

"This is a complicated statute dealing with complicated technology, and we'll have to see how the legislative process moves forward." Gonzales said. "This is a new kind of war and there are now new kinds of technologies, and the president has to be able to make use of new technologies."

Pressed regarding the surveillance program's constitutionality, Gonzales said: "I am confident of the constitutionality of everything we do as an administration."

The plan received skeptical approval from Democrats.

Sen. Patrick Leahy, the top-ranked Democrat on the Senate Judiciary Committee, said the negotiated plan might not go far enough.

"What the president has said is that he will do something that he could do today if he really wanted to, and that is have the FISA court look at the legality of what he claims is legal and what most people feel is illegal. But he will do it if the House and Senate pass a bill specifically saying what he wants it to say. It is still a long step from checks and balances," said Leahy, D-Vt.

Sen. Dianne Feinstein, D-Calif., said Specter's agreement with the White House raises the "thorny question" about whether the content of conversations should be subject to individual courts warrants.

"I really need to see the bill," said Feinstein, one of a select group of lawmakers who has been fully briefed on the monitoring operations.

Rep. Ed Markey, D-Mass., also reacted tepidly to the announcement, called it a starting point.

"This should not exempt the secret program from thorough congressional scrutiny. The closed-door deal reached with Senator Specter should be the beginning of full congressional review of the program and any legislation that is based on the agreement, not the end of the story," Markey said.

"The secret domestic surveillance program has operated in the shadows. Now is the time for the courts and the Congress to shed some light on it," he added.

The American Civil Liberties Union's chief released a statement critical of the plan, calling it "nothing short of a capitulation by Chairman Specter to the White House."

"The 'review' contained in the bill is nothing more than a sham. The president could still choose to ignore the optional court oversight on the program. This new bill would codify the notion that the president is not bound by the laws passed by Congress or the Constitution. It would reward his abuse of power," ACLU Executive Director Anthony Romero said in a written statement.

Should the FISA court approve the terror surveillance program, that should be the end of the controversy, Specter said. If not, it could go to the highest court in the land.

"The Supreme Court is the ultimate decider. I wouldn't be surprised if it doesn't end up there," he said. Specter said the announcement was unrelated to the recent Supreme Court decision in Hamdan v. Rumsfeld, which concluded that detainees held by the United States at Guantanamo Bay, Cuba, and elsewhere, must be subject to Geneva Convention rules unless Congress comes up with a law to deal with this particular brand of combatant.

FOX News' Trish Turner, Ian McCaleb and Rich Johnson and The Associated Press contributed to this report.