State police spokesman Sgt. Chad Pierce says Wolff got a ride to a picnic area and fishing spot and was last seen at about 5 p.m. on June 7.
The Dalton Canyon Picnic area is about six miles north of Pecos in a rugged section of the Santa Fe National Forest.
Police began searching Thursday when Wolff did not return.
Wolff has written songs that have been recorded by Johnny Gill, Taylor Dayne, Aretha Franklin and Atlantic Starr, among others. He also wrote two Billboard Hot 100 No. 1 hits -- "Straight Up" and "Cold Hearted" -- for Paula Abdul, who has been tweeting about Wolff's disappearance and praying for his safe return.
Wolff's wife, Stacey Piersa, posted the below statement to her private Facebook page late Tuesday and authorized a friend to share the post with Billboard.
It is with a heavy but hopeful heart that I write this post. My husband, Elliot Wolff, went hiking by himself on Tuesday, June 7th. When I did not hear from him as expected, I went looking for him and alerted the New Mexico State Police. Immediately they mobilized search and rescue efforts. I have spent the past week with so many wonderful and giving volunteers searching for Elliot. He is an experienced outdoorsman and has been camping/hiking by himself many times before. Our family is praying with each day that we will find him, perhaps injured, but alive. I know how many of you love Elliot and your thoughts and prayers are appreciated and needed right now. Many of you may try to reach out to me, but please understand, and don't take it personally, if I'm not able to get back to each and every one of you. Our #1 priority is continuing these search efforts. I delayed posting on social media for a few days because I was certain we would find Elliot. Unfortunately, with each passing day, our hope is diminishing. If anyone has any information please reach out to the New Mexico State Police (505) 827-9311.