His intervention, made on the club's website, follows frenetic speculation about the future of Rangers and comments by Dave King, a former director of the club.
It also comes as the main Rangers supporters' groups issued a vote of no confidence in the Ibrox board, adding that they would ask King to set up a trust where "fans can place our season-ticket money to be released to the club on agreed terms".
A statement released by the Union of Fans, on behalf of the Rangers Supporters' Trust, Rangers Supporters' Assembly, Rangers Supporters' Association, Blue Order, Union Bears and Sons of Struth, revealed it was "deeply concerned, once again, about the direction our club is being taken."
King, a South African-based businessman, has called on supporters to pool their season-ticket money into a trust and use their influence to campaign for a voice in the boardroom. Disaffection among some supporters has also been heightened by the details of a loan facility offered to the club by Sandy Easdale and Laxey Partners, the single largest shareholder. The latter will receive a £150,000 premium on their loan, payable in cash or shares.
Wallace, who was appointed in November, is in the midst of a 120-day review of the club's finances and operations in a bid to cut the spending that saw Rangers post an operating loss of £14.4m last season.
King's call over season tickets was described earlier this week by the club as "potentially damaging and destabilising" and last night Wallace stepped up the rhetoric. "In recent days there has been considerable comment and speculation about the financial position of the club and the motives of individuals managing it following the announcement of short-term financing being put in place," Wallace said.
"Much of the comment and opinion is unfortunately ill-informed and directed at undermining the club and the considerable efforts that are taking place to rebuild it following several years of mismanagement."
This could be taken as a swipe at King, who was on the board of Rangers under Craig Whyte.
"It is extremely concerning that public statements are being made that are factually incorrect," Wallace continued. "If left unchallenged, they would damage the reputation of the club and individuals who are committed and working every day to rebuild it."
The chief executive, who admitted there could be "scepticism"among Rangers supporters, said he would show improvements to "all areas of the club" in due course.
He addressed the issue of the refusal of alleged interest-free loans by saying: "This is wholly untrue and supporters need to know this."
On the sales of season tickets, Wallace said: "Further comment about withholding future ticket revenues is also damaging to the operation of the club which, in common with many others, operates on a cyclical basis."
On the club's need for a cash injection, he said: "We are putting in place a business structure and operational model that will protect and develop Rangers Football Club for future generations.
"We know the club will require investment in the future but until we have addressed the problems and deficiencies of the past, it would be foolhardy to seek additional investment without a clear plan of how to use it."