The Electronic Privacy Information Center (EPIC) has filed an objection to agreements Google has reached over its social network Buzz because it is not one of the beneficiaries of the privacy fund set up by Google.
EPIC is a public interest research center in Washington, D.C. It was established in 1994 to focus public attention on emerging civil liberties issues and to protect privacy, it says in its website.
The US privacy group has demanded $1.75m (£1.09m) of the $8.5m (£5.2m) fund, claiming that it is a more independent group than some of the beneficiaries.
Last week, Google reached an agreement with the US Federal Trade Commission (FTC), after an investigation found that Google was wrong to use personal information of Gmail users to create Buzz without seeking prior permission of the users.
Google agreed to undergo a privacy audit for the next 20 years along with a fine.
EPIC, which filed the successful complaint with the FTC that led to the agreement, and some other groups say that the proposed settlement does not satisfy the "cy pres" requirement.
They note that many organisations proposed by Google are currently funded by Google.
EPIC said in its website, "Cy pres" (as near as possible) is a legal doctrine that allows courts to allocate funds to protect the interests of individuals when there is a class action settlement. In such cases, courts are often concerned about collusion between attorneys that produces quick settlements and does not protect the interests of the class members.