NEW YORK — Her soon-to-be ex-husband Rex Heuermann is accused of four of the Gilgo Beach murders — but Asa Ellerup says she still gives him “the benefit of the doubt” in the headline-grabbing case.

“I will listen to all of the evidence and withhold judgment until the end of trial,” Ellerup said in a statement released late Wednesday. “I have given him the benefit of the doubt, as we all deserve.”

Ellerup also said her heartfelt sympathies go out to the victims and their families. “Nobody deserves to die in that manner,” she said in the statement released by her lawyer, Robert Macedonio.

In the statement, Ellerup said she does not believe Heuermann is capable of committing the crimes he is charged with.

Ellerup, 60, filed for divorce six days after Heuermann was nabbed for the cold-case murders of three Long Island sex workers — Megan Waterman, Melissa Barthelemy and Amber Costello. Heuermann, was indicted on a fourth murder in January— the killing of Maureen Brainard-Barnes of Norwich, Conn.

Authorities found the remains of the women, known as the “Gilgo Four,” within a one-mile radius on Ocean Parkway near Gilgo Beach in December 2010 while cops searched for Shannan Gilbert, another sex worker who went missing in the area.

Heuermann, a Long Island resident and father of two who had an architectural practice in Manhattan, was arrested July 13. He has pleaded not guilty to murder and other charges related to the killings.

The murders of all four victims took place at times when Ellerup and their children were traveling out of state, which prosecutors have said allowed Heuermann “unfettered time” to execute his plans without worrying his family would find out.

“We have said consistently, since day one, July 13th was a surprise to Asa Ellerup and her children. This life that existed, or may have existed, they were completely unaware of,” Macedonio previously said outside the courtroom after Heuermann’s January hearing.

Ellerup visits her estranged husband weekly at the Suffolk County Jail in Riverhead, L.I., according to her lawyer. Victoria Distefano, a spokeswoman for the Suffolk County Sheriff’s Office, said Ellerup has signed into jail seven times.

A spokeswoman for the Suffolk County district attorney’s office declined to comment on Ellerup’s statement.

Heuermann is set to return to court on April 17.