The petitions to the Foreign Intelligence Surveillance Court followed similar petitions by other Web-related technology companies, including Google Inc. and Microsoft Corp.
Google and Microsoft separately filed additional legal briefs Monday asking the court to lift a gag order and let them disclose more information.
The court -- known as the FISA Court, after the Foreign Intelligence Surveillance Act that established it -- issues warrants for collecting foreign intelligence inside the United States.
All four tech companies, in rare coordinated but separate lawsuits, say they want permission to reveal the aggregate number and nature of the national intelligence requests to respond to growing public concern and to regain the trust of users, the Los Angeles Times reported.
"We believe that the U.S. government's important responsibility to protect public safety can be carried out without precluding Internet companies from sharing the number of national security requests they may receive," Yahoo! General Counsel Ron Bell said in a blog post.
The tech companies, prevented from disclosing information under national security rules, say they also want permission to correct false allegations and incorrect news reports about what they supply to the FBI for National Security Agency use. They argue their constitutional free-speech rights are being violated.
Yahoo! alleges The Washington Post and British newspaper The Guardian were factually incorrect when they reported June 15 the NSA's top-secret PRISM mass electronic surveillance data-mining program directly tapped into servers of major Internet service providers to collect information.
The PRISM program, whose existence was leaked starting in June by former NSA contractor Edward Snowden, gathers stored Internet communications from various Web and phone companies.
"Yahoo!'s inability to respond to news reports has harmed its reputation and has undermined its business not only in the United States but worldwide," Yahoo! says in its motion.
The Post and Guardian had no immediate comment on the Yahoo! assertion of false reporting.
In a bigger sense, "Yahoo! has been unable to engage fully in the debate about whether the government has properly used its powers, because the government has placed a prior restraint on Yahoo!'s speech," the Sunnyvale, Calif., company's motion says.
Prior restraint, or censorship before a communication takes place, is considered unconstitutional except in extraordinary circumstances, such as to protect national security, the U.S. Supreme Court has said.
Yahoo! noted in its filing an August decision by National Intelligence Director James Clapper to release the number of people targeted by FISA Court orders "undermines any argument that prohibiting Yahoo! from publicly disclosing the same data would harm national security."
Facebook submitted similar motions Monday after saying negotiations with the government had fallen apart.
The Justice Department had no immediate comment on the lawsuits.