They argued children are less able to distinguish advertisements from other online content and are especially vulnerable to manipulation.
Facebook acknowledged earlier this month that it is testing features that would allow young children to access the site. The company would have to navigate the Children’s Online Privacy Protection Act (COPPA), which restricts the ability of websites to collect information from children younger than 13.
The groups noted that millions of children already lie about their age to use Facebook, and they applauded the social media company for trying to address the problem.
They said parents should be able to control their children's actions on Facebook, including giving approval for every action before it becomes public on the site.
Andrew Noyes, a Facebook spokesman, said the company welcomes the groups' recommendations.
"Enforcing age restrictions on the Internet is a difficult issue, especially when many reports have shown parents want their children to access online content and services," he said.
—Updated at 9:36 p.m.