In the court filings, the organisations said that there was "no adequate justification" for the FBI to continue to withhold the information.
They added that they did not seek information that would jeopardise national security.
The groups sued the FBI last year.
Associated Press, Vice Media and Gannett, the parent company of USA Today, are seeking to learn more about the circumstances surrounding the event.
The FBI has never named the security firm or group of hackers who helped unlock the phone, which was used by killer Syed Rizwan Farook.
The process would have involved finding a way to bypass the passcode on a locked phone. In normal circumstances, if 10 incorrect attempts at the code are made, the device will automatically erase all of its data.
Security of millions
"While it is undisputed that the vendor developed the iPhone access tool, the government has identified no rational reason why knowing the vendor's identity is linked in any way to the substance of the tool, much less how such knowledge would reveal any information about the tool's application," lawyers for the news organisations wrote in the filing to the US District Court in Washington.
"Release of this information goes to the very heart of the Freedom of Information Act's purpose, allowing the public to assess government activity - here, the decision to pay public funds to an outside entity in possession of a tool that can compromise the digital security of millions of Americans."
Farook and his wife killed 14 people in the Californian city in December 2015.
In February, a court order demanded that Apple help unlock the phone, something which Apple resisted, saying said it was unable to do so.
It added that it hoped that the government would share with the company any vulnerabilities of the iPhone that might come to light.
There was speculation that the FBI paid at least $1.3m (£1.05m) to break into the phone, based on calculations following comments by FBI director James Comey who said that the agency had paid more to get into the phone than he "will make in the remaining seven years" in his post.
He added that it was worth it, even though no details of what was found have been released.