The Federal Government proposed new rules today to protect the privacy interests of children on the Internet.

The rules, prepared by the Federal Trade Commission, would require commercial Web sites to get parental consent before seeking information from children under 13. It would also require the sites to post notifications about what they do with any information obtained from children.

The proposal comes after a new law expanding the agency's authority on privacy issues. That legislation moved through Congress quickly last fall after studies by the Government and experts showed that the vast majority of Web sites collect personal information from consumers and children and that very few companies provide notice about what they do with such information.

''Kids are a particularly vulnerable audience,'' said Robert Pitofsky, chairman of the Federal Trade Commission. ''You mix the invasions of privacy with kids and you have a particularly combustible mix.''