DeLay is under indictment for violating campaign fund-raising laws and has temporarily resigned his leadership post.
"I think we're going to let the justice process work its way through," Graul said.
Green said returning the money could amount to breaking the law.
"And as we understand it, it would actually be illegal to do what they are calling for," Green said.
Joe Winecke, chairman of the Wisconsin Democratic Party, began calling for Green to divest the money last week. He stepped up the pressure Thursday by unveiling the Web site, http://www.dirtygreen.com, which describes Green's "ethically challenged dash for cash."
"It goes beyond dollars and cents into where are your values," Winecke said. "In Mark Green's case it's pretty clear to me that he values his relationship to Tom DeLay."