Late last year, EFA called for warrants to be mandatory when access to metadata is sought.
The organisation was particularly concerned about inadequate protections for journalists.
Parliament originally restricted warrantless access to what EFA describes as "a carefully chosen list of agencies," but since then a much broader range of agencies have sought such access.
"The restricted list of agencies able to access telecommunications data is the first and only meaningful limitation on the previously unfettered access to this information by any public or quasi-public agency," said EFA executive officer Jon Lawrence.
"If the Attorney-General is serious about the integrity of his legislation and about protecting the civil liberties of all Australians, then he must act swiftly to reject the majority of these applications."
The EFA's position is that the requirement for a warrant to obtain access to metadata should cover the entire population.
"There are many other privileged communications that also deserve protection, in addition to the critical need to facilitate effective whistle-blowing. The only effective means to protect such communications is for the warrant requirement to be extended to the entire population," said Lawrence.