Smith was a renowned supporter of manager Ally McCoist, while Green has had a number of clashes with the Rangers boss, the most recent of which came on Saturday, leaving fans concerned over a potential power struggle at the club.
"The Rangers Supporters' Association, Rangers Supporters' Assembly and the Rangers' Supporters Trust are extremely concerned with current events at our club. Walter Smith's resignation is a matter of deep anxiety and we trust that Walter will give supporters a detailed statement outlining his reasons for leaving," read a joint statement.
"The recent request for an EGM (Extraordinary general meeting) to replace key personnel would suggest our concerns are shared by other significant shareholders. We would therefore urge the board of Rangers Football Club to agree to allow the EGM to proceed as soon as possible to enable the thousands of fans who have invested in the club to hear all sides in an open forum.
"In the meantime, we have requested an urgent meeting with the chief executive in order to keep our members as informed as possible."
Rangers were knocked out of the Scottish League Cup in the first round on Saturday, losing 2-1 to Forfar after extra time.