The musician, 36, has not been seen since leaving the Dakota Hotel in South Queensferry at 1am on Wednesday.
His brother and bandmate Grant Hutchison said the family felt helpless but that the support they have received had been incredible.
Speaking to Radio X, he said: “We’ve been coping as well as we can really, all the family are together and just supporting each other and doing all we can to try and let Scott know that we are here for him and that we love him.
“We just all feel a little helpless but the support has been incredible.
“It really genuinely does keep us going and keeps us feeling positive about the situation to know that there is that many people out there who care so much about Scott and want us to know that and want him to know that as well.
“If he has access to get online and he has seen any of it then it’s important that we keep sharing that to let him know he is loved and that we just want him to come back.
Asked if he had a message for his brother, he said: “Just come back. There’s nothing that is so insurmountable that we can’t figure it out together and help you to get better.
“We’re all here for you and we all love you very much. If you can see the support online as well, just know that everyone loves you very much and we just want you to come back and be safe.”
Messages of hope were posted on social media from friends, family and fellow musicians, including Gary Lightbody from Snow Patrol.
There was also support from authors Irvine Welsh and Christopher Brookmyre, and radio presenter Edith Bowman.
Hutchison is described as white, 6ft tall with a stocky build, dark hair and a thick beard.
He was last seen wearing a dark baseball cap, navy blue hooded jacket, grey or khaki trousers and white trainers.
Police Scotland said there was no update on the search for the singer, who lives in Dennistoun, Glasgow.
Anyone with information should contact officers at Drylaw Police Station via the 101 number.