While conceding season ticket sales were slow, he insisted there was "no threat to the future stability of the club".
In a question and answer session on the Twitter social networking site he said he understood why fans mistrust what has happened at the club in recent years and that he and the board were "working hard" to earn their "trust and respect".
He said the formation of a new fan liaison board was expected to be in place in the next few months and a new fan membership scheme is planned for next season.
When questioned whether he cared about the club or whether it was just another job, he replied: "I absolutely care about the club personally and professionally. We have a big job to do here and I am proud to be Rangers' CEO."
Mr Wallace took to Twitter as part of what he described as an "ongoing Ready To Listen fan engagement programme".
It comes days after the Rangers Union Of Fans launched a website to allow supporters to pool cash that it says will only be released to the club once security over Ibrox Stadium and Murray Park has been granted.
With hundreds of questions asked of the executive, Mr Wallace spent 90 minutes answering 15 selected questions from fans.
Recurring topics he did not tackle included the identities of those behind the institutional investors Blue Pitch Holdings and Margarita Funds. Together they hold more than 10% of the shares in the operating company Rangers International Football Club plc.
But Mr Wallace did not try to avoid the questions asking him to justify his £315,000 a year salary with 100% bonus. He said: "Any bonus I may be awarded would be discretionary, based on a mix of company and personal performance.
"This would be determined by the remuneration committee and any bonus for this year would only reflect the time I have been here."
The club has always said the pay and bonuses were in line with the requirements of AIM, the London Stock Exchange's international market for smaller growing companies, and that employing key executives of appropriate calibre was "vital to the board's strategy to both reposition Rangers at the top of Scottish football and to compete regularly in Europe".
When asked why board bonuses are being discussed or taken when redundancies are in the pipeline he said: "We are restructuring areas to better position us for future growth. As part of this, a small number of roles may be affected.
"We are working with everyone potentially impacted to identify if there are any potential alternatives for them."
Mr Wallace was also asked how difficult his job was in the face of 'misinformation' in the media. He replied: "Yes it is a challenge, but the important thing here is to lead the rebuilding of the Club."
When asked if he understood why fans have no faith in the board, he replied: "I can understand the fans having mistrust after what has happened to the club in recent years.
"We have given fans details of operations over the past two years and outlined the major areas of income and expenditure.
"The board is committed to the long term development of Rangers and is working hard to earn the trust and respect of our fans."
While insisting there was "no threat" to the future stability of the club, he added: "Like any football club, Rangers relies on the support of its fans. If fans continue to support the club in the way they have, we have a great platform to build for the future."
While the early findings of a Rangers Supporters Trust poll suggested as many as 77% of members have not purchased a season ticket for next term, Mr Wallace reiterated that sales were "slow".
But the executive said it was "understandable given the assurance fans have sought about the stability of the club".