"The threats we face from terrorism, proliferation and cyberattack, among others are real, and they will continue," Feinstein said in the statement. "Intelligence is necessary to protect our national and economic security, as well as to stop attacks against our friends and allies around the world."
She said "more can and should be done" to increase transparency of the surveillance and build public support for privacy protections.
But Rep. Adam Schiff, a Democrat who sits on the House Intelligence Committee, said the legislation allows the bulk collection to continue under certain safeguards. He called the safeguards a positive first step but said the NSA should stop sweeping up Americans' phone records and only obtain those that are connected to a specific terror plot.
Privacy advocates who have long called for the end of broad government snooping objected to the bill, which they said would merely legalize the surveillance that the NSA has quietly undertaken since 2006.
David Segal, executive director of advocacy group Demand Progress, said "Lawmakers must immediately recognize this legislation for the sham that it is and reject it outright."
The Senate intelligence bill rivals one put forward earlier this week, by House and Senate judiciary committees, that would eliminate the phone data collection program that was revealed earlier this year in classified documents that were released to the media by NSA leaker Edward Snowden.
The dueling legislation means that Congress ultimately will have to decide how broadly the U.S. government can conduct surveillance on its own citizens in the name of protecting Americans from terror threats.
Polls indicate that Americans widely oppose the surveillance program.
Meanwhile, the NSA issued a more forceful statement rejecting reports that it illegally collected millions of records from communications links between Yahoo and Google data centers around the world.
The Washington Post, citing documents obtained from Snowden, has reported that the NSA sent records from the companies' internal servers to data warehouses at the agency's headquarters.
The NSA said such reports have "misstated facts, mischaracterized NSA's activities, and drawn erroneous inferences about those operations." In a detailed statement, the agency said its activities are conducted in accordance with law and policy. And it said the data collection goes after valid foreign intelligence targets that often use communications over satellite links, microwave towers and fiber-optic cables.
"U.S. service provider communications make use of the same information superhighways as a variety of other commercial service providers," the agency said. "NSA must understand and take that into account in order to eliminate information that is not related to foreign intelligence."
Under normal procedures, the NSA is required to sort data based on relevant potential threats and seek additional legal authorities to access the information if the communication involves an American.
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Associated Press writer Lolita C. Baldor contributed to this report.
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