The Suffolk nonprofit hired by the county to monitor registered sex offenders has sued a Cincinnati registered sex offender, accusing him of defaming the group with his online posts.

Parents for Megan’s Law filed a lawsuit in Suffolk state Supreme Court in Central Islip on Tuesday, claiming Derek W. Logue, who runs a support website for sex offenders, made “false disparaging statements about the integrity” of the Ronkonkoma-based group on his Twitter account and an online news forum.

Logue, who was served with court papers as he protested outside of the nonprofit’s Comac Street office on Wednesday, contends his posts accusing the group of receiving “kickbacks” are protected by the constitutional right to free speech.

The legal dispute comes as the group, which tracks the addresses of more than 1,000 registered sex offenders and provides counseling services to sex-abuse victims, renegotiates its three-year $2.7 million contract with Suffolk. It is set to expire at the end of the month.

Vanessa B. Streeter, a spokeswoman for Suffolk County Executive Steve Bellone, said the county plans to renew the group’s contract, but is “still working out the terms.”

At the center of the lawsuit is a Feb. 23 post Logue wrote responding to an online article about an upstate Broome County lawmaker’s call to increase the 20-year period Level 1 sex offenders must remain on the state’s registry to 25 years.

“This is what is known as ‘moving the goal post,’” Logue wrote in the comments section of Binghamton’s FOX 40 WICZ TV news website. “ . . . The REAL reason the state is pushing this is because Parents for Megan’s Law gets millions of dollars in kickbacks.”

In that post, and on his Twitter account, Logue questioned whether the agency’s funding went to “padding” the pockets of the Broome County legislator pushing for the increase, a claim the nonprofit’s attorneys say is “false” and made “with reckless disregard for the truth.”

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Laura Ahearn, founder and executive director of Parents for Megan’s Law, said she couldn’t comment on the lawsuit, and referred questions to the group’s pro-bono attorneys at the Mineola law firm of WeitzPascale.

“You can’t go around defaming innocent organizations that are here only to defend children, the elderly, the disabled,” said attorney Brian C. Pascale, a partner at the firm.

Logue, who pleaded guilty in 2000 to first-degree sexual abuse against an 11-year-old girl in his home state of Alabama, according to court records, said he has traveled to other cities to protest sex-offender residency restriction laws.

He said he came to Suffolk to protest the county’s tracking program because he believes municipalities should focus on funding “rehabilitative” programs that help offenders reintegrate into society.

“They’re trying to silence me for speaking up,” Logue said in an interview. “It’s easy to go after and dehumanize a group that’s invisible in the eyes of society.”

Logue, who carried a sign that read “Parents for Megan’s Law: Stop Supporting Myths for Money,” said he tried to stage a larger demonstration. He said he sent letters to 300 Suffolk registered offenders encouraging them to come out and protest, but only one showed up.

Parents for Megan’s Law is also defending itself against a federal lawsuit filed last month by a Suffolk registered sex offender, who claims the nonprofit violated his civil rights by interrogating him at his house.