The Electronic Frontier Foundation (EFF) says that "more is needed" from Facebook to address privacy criticisms.
In a blog post, the civil liberties group praised Facebook for a "great first step" towards giving members of the site more control over their data.
However, it warned members against choosing the site's recommended privacy control setting.
Doing that shares "a substantial amount" of information widely, the group claimed.
"The changes are pretty good, though more is needed," wrote Kevin Bankston, senior staff attorney at the EFF.
Facebook's decision to enable users to either select one setting to cover all information or to choose individual settings for different types of information (such as making photos more private than status updates for example) struck a "good balance" said Mr Bankston.
The foundation still had concerns about third-party access to individual profile information though.
"Facebook is a site that many people joined because it was a more private alternative to sites like MySpace and Twitter," wrote Mr Bankston.
"To keep in line with user expectations, no information should be required to be publicly available."
Simon Davies, director of Privacy International, also questioned whether Facebook had gone far enough with its new arrangements.
"I don't know whether these reforms on their own are going to satisfy the overwhelming force for change and reform," he told the BBC.
"Perhaps people are unable to reconcile the two worlds they live in," he added, explaining that the concept of Facebook friendship is not as arbitrary as it is in face-to-face life.
"Facebook has a monolithic approach to friendship - but as you build friendship you build the privacy along with it. Perhaps a privacy model should follow that," he said.
Amichai Shulman, chief technology officer at net security firm Imperva, said that services such as Facebook were ultimately designed for information sharing.
"The essence of social networks is to provoke solicited, and unsolicited, interactions between individuals," he said.
"Privacy does not coincide with the interests of Facebook creators or with the attitude of many Facebook users."
However the site must now fight to regain the trust of its members, he added.
"Today, Facebook is at a serious crossroads. If it continues giving the impression that user privacy is a football, it risks further alienating them."