NEW YORK (CNN) -- Police say a man in custody has implicated himself in the 1979 disappearance of 6-year-old Etan Patz, whose disappearance exactly 33 years ago Friday helped raise awareness of missing children after authorities tried a then-novel approach of putting the boy's face on milk cartons.

However, a law enforcement source told CNN Thursday that the man's claims about the boy are being treated with "a healthy dose of skepticism."

The man "has made statements to NYPD detectives" regarding Etan's disappearance and death 33 years ago, Police Commissioner Ray Kelly said in a statement. Authorities will divulge more details later Thursday, he said.

The man, who was undergoing questioning, was picked up Wednesday in New Jersey, two law-enforcement sources told CNN.

He claims to have played a direct role in Etan's death. The man's statement is "a good lead," the source said, but it was unclear where this will take the case.

The man, who has not been identified, lived and worked in the same Manhattan neighborhood where the Patz family lived, the source said.

Investigators have looked at the man before in connection with the case, according to the second source, and his information is being treated very cautiously.

Renewed attention over the Patz case sprung up last month when investigators scoured a Manhattan basement in search of evidence, but produced no obvious clues.

A spokeswoman for the Manhattan district attorney's office, which reopened the case in 2010, declined to comment on the recent development.

Etan's disappearance received national attention and, along with other high-profile cases, helped trigger a national movement that focuses on missing children.

He went missing on May 25, 1979, a block from his home in the New York neighborhood of SoHo. It was the first time he had walked to his school bus stop by himself.

His mother, Julie, learned after her son failed to return home from school that he hadn't been in classes that day. After calling the school and Etan's friends, she called police.

The boy was officially declared dead in 2001 as part of a lawsuit filed by his family against a drifter, Jose Antonio Ramos, a convicted child molester acquainted with Etan's baby sitter.

A judge found Ramos responsible for the boy's death and ordered him to pay the family $2 million -- money the Patz family has never received.

Though Ramos was considered a key focus of the investigation for years, he has never been charged in the case. He is serving a 20-year prison sentence in Pennsylvania for molesting another boy and is set to be released this year.

A source has previously said investigators wanted to expand the pool of possible suspects beyond Ramos.

Parents Stan and Julie Patz still live in their SoHo home and have not commented on the new developments.

Lisa Cohen, author of "After Etan: The Missing Child Case That Held America Captive," told CNN earlier that "the family's been living through this for 33 years. They've had many moments like this. They've learned how to deal with it."

The Patz case was among those that drew national attention to missing children. Police helped put his face on thousands of milk cartons. Later, billboards and fliers calling attention to missing children became common.

Just weeks after Etan disappeared, an attacker abducted the first of more than 20 children to be kidnapped and killed in Atlanta. A suspect in that case was arrested two years later.

In 1981, the abduction and slaying of 6-year-old Adam Walsh from a Florida shopping mall also made national headlines.

In 1984, Congress passed the Missing Children's Assistance Act, which led to the creation of the National Center for Missing & Exploited Children.

President Ronald Reagan named May 25, the day Etan went missing, as National Missing Children's Day.

CNN's Susan Candiotti contributed to this report.