The Scottish Premier League last week appointed an independent commission to determine whether Rangers breached rules in relation to Employee Benefit Trust (EBT) payments and arrangements for players between 2001 and 2010.
In a statement released to Press Association Sport, Murray said: "During my stewardship of Rangers no rules were breached or circumvented and I reject and resent any suggestion that anything was done which amounted to cheating."
One of the more severe sanctions the Ibrox side could face if found guilty is the stripping of championship titles, a punishment the club have said they would strenuously challenge.
Murray added: "I cannot be anything other than angered at the suggestion Rangers should be stripped of titles or other competition victories."
Ally McCoist has already declared he would never accept Rangers being stripped of titles and he believes the SPL are wasting their time with the investigation.
The manager said: "I'm under the impression there are absolutely no dual contracts.
"I've been told it's probably a complete waste of time."
Rangers are set to play their first game at Ibrox on Tuesday since the club was consigned to liquidation and voted into the Irn-Bru Third Division.
Speaking ahead of the visit of East Fife in the Scottish Communities League Cup, McCoist said: "I'm looking forward to seeing a big crowd and I believe the fans will come out and support, I really do."