Investigators on Long Island on Tuesday morning will announce a “significant development” in the investigation of Rex Heuermann, the Massapequa Park architectural consultant accused in the Gilgo Beach serial killings.

The Suffolk County district attorney’s office said on Monday that the announcement would happen after a 9:30 a.m. court hearing for Mr. Heuermann, but did not provide any more details.

Authorities have already charged him in the murders of six women, including one found in Southampton. They have been working intently to secure indictments in the killings of five other people whose remains were found near Gilgo Beach.

Only two of those victims have been identified: Valerie Mack and Karen Vergata. In September, investigators held a news conference seeking information on one of the unidentified victims, a young Asian man found wearing women’s clothing.

Investigators have been seeking to tie Mr. Heuermann to a DNA profile of Ms. Mack, whose relatives indicated in recent days that the Suffolk authorities had been in touch with them.

“We’re just processing so many emotions right now,” her father, Edwin Mack, said by phone last week from his southern New Jersey home, adding that he was unsure whether he would attend the Tuesday hearing.