The Californian telecoms company thought to be behind a stunning court victory that has blown a hole in the FBI's highly secretive system for collecting US citizens' private data has hailed the "significant" legal breakthrough.

Credo, based in San Francisco, spoke out after a federal judge ordered the US government to stop issuing what are called "national security letters" – demands for data that contain in-built gagging clauses that prevent the recipients disclosing even the existence of the orders or their own identity.

In a carefully worded release, the firm fell short of revealing itself as the instigator of the legal action that resulted in Friday's development. But it is understood by the Guardian that the telecommunications firm was indeed the unnamed litigant behind the action.

Michael Kieschnick, chief executive of Credo Mobile, hailed the judge's order as "the most significant court victory for our constitutional rights since the dark day when George W Bush signed the Patriot Act".

It is extremely rare for a telecoms company to challenge the system of national security letters, or NSLs, which have mushroomed since 9/11 under the Patriot Act. Credo, a subsidiary of Working Assets Inc, that directs some of its profits to support civil liberties groups, has been a long-standing advocate for reform of the NSL.

It is believed to be the company behind a May 2011 lawsuit in which the FBI was sued for breach of its rights after the company was served with a federal demand for private data belonging to its customers. The FBI shot back by counter-suing the company.

The lawsuit was made anonymously, with the name of the company redacted from court papers made available to the media. But last July the Wall Street Journal conducted an analysis of the likely telecoms companies that could have brought the legal action, and concluded that the litigant was probably Credo.

In her ruling, Judge Susan Illston declared the NSLs unconstitutional as they breached the first amendment rights of the parties being served the orders.

Kieschnick said: "This decision is notable for its clarity and depth. From this day forward, the US government's unconstitutional practice of using national security letters to obtain private information without court oversight and its denial of the first amendment rights of national security letter recipients have finally been stopped by our courts."

NSLs have been an increasingly important part of the US government's approach to counter-terrorism, though their growing use has been matched by mounting unease on the party of civil libertarians.

Last year the FBI sent out more than 16,000 of the letters relating to the private data – mainly financial, internet or phone records – of more than 7,000 Americans.

Previous court action has led to the FBI being accused of abusing its powers under the NSL statute by issuing the letters far more extensively than in the limited counter-terrorism situations for which they were devised.

The letters are among the most secretive tools of any deployed by the US state. The demand for data comes with a gagging order attached – meaning that the recipient of the NSL is not allowed even to discuss the letter in public.

As an additional affront, civil liberties groups say, the FBI is allowed to issue the letters without approval from a judge. Only the green light of a local FBI chief is required.

The judge's order will not go into immediate effect as she built in a 90-day delay to allow the government to appeal. The telecoms company was represented in the case by the Electronics Frontier Foundation, a non-profit group that advocates for public rights in the digital world. In a statement, the EFF's senior staff attorney Matt Zimmerman said the court order had exposed the constitutional shortcomings of the NSLs.

"The government's gags have truncated the public debate on these controversial surveillance tools. Our client looks forward to the day when it can publicly discuss its experience."

The foundation's legal director Cindy Cohn added that the judge had also highlighted the first amendment as a protection for the public against executive surveillance power. "The NSL statute has long been a concern of many Americans, and this small step should help restore balance between liberty and security."

• This article has been amended since publication.