Though Facebook (Nasdaq: FB) bans children under 13, millions of them have profiles on the site by lying about their age.

Now, the company is testing out ways to allow younger kids on its site without needing to lie. It would be under parental supervision, such as by connecting children’s accounts to their parents’ accounts. That would allow Facebook to comply with federal regulations regarding children under 13 online.

“Many recent reports have highlighted just how difficult it is to enforce age restrictions on the Internet, especially when parents want their children to access online content and services,” Facebook said in an e-mailed statement. “We are in continuous dialogue with stakeholders, regulators and other policymakers about how best to help parents keep their kids safe in an evolving online environment.”

In May 2011, Consumer Reports said a survey showed that Facebook had 7.5 million users who were younger than 13 in the prior year, in violation of the website’s policies. More than 5 million of the users were under age 11, the watchdog group said.

The Wall Street Journal reported earlier that Facebook was developing technology to let younger children use its website under parental supervision.

The Wall Street Journal reported on the development in Monday’s editions. It could be a long way off, or never get implemented, as happens with many features that Facebook tests.

Relaxing rules that bar kids from joining the world’s largest social network might help Facebook lure advertisers that are eager to reach Web surfers at an early age. Facebook – already accused by regulators of failing to protect members’ privacy – must be careful to shield young users and keep them safe online, said U.S. Representative Mary Bono Mack, a California Republican.

“In developing this new technology, Facebook needs to proceed with an abundance of caution,” said Bono Mack, who heads a House Energy and Commerce subcommittee that has looked at online privacy issues, in an e-mailed statement. “Very strict privacy protocols must be in place before younger children are allowed on social-networking sites. Before this happens, Facebook also has a responsibility to expand its efforts to educate parents and preteens about the dangers of cyberspace and how to use the Internet and social networking in a safe way.”

(Bloomberg news contributed to this report.)