Wallace was speaking from Toronto, Canada where he was attending the annual convention of the North American Rangers Supporters Association (NARSA).
He took part in a question and answer session with supporters on Saturday but is understood to have been vague when asked about the numbers renewing their season tickets.
Wallace had warned in April that Rangers' ability to continue as a going concern would be placed in jeopardy "should the club suffer a substantial decrease in season ticket income in the next two months".
The Union of Fans group has been urging supporters not to renew unless they are given assurances from directors about the long-term future of the club and have also requested security over the club's Ibrox stadium and Murray Park training ground. Neither has so far been received. Estimates in recent weeks on how many tickets have been sold have ranged from 5000 to 20,000, with the club yet to make a formal announcement to the AIM market. It is also thought the board is yet to pay back the £1.5m in loans borrowed from two shareholders, Sandy Easdale and George Letham, which they were required to do as soon as they have raised sufficient income.
Despite the uncertainty, Wallace remains bullish about the future, reiterating his previous claim that there was no prospect of Rangers going into administration for a second time. He said that fans should feel "confident and comfortable" about the club's future.
"Almost since the day I came to Rangers, we've been operating in an environment where there have been consistent questions about the financial stability of the club," he told the club website. "I've repeatedly come out and said there's no threat of administration and we've built a very solid base now which we're moving forward from. The fans should take reassurance and comfort from that.
"We are moving in a way that allows us to grow and develop the business. The long-term financial stability of the business is well in hand and we are in a good place now. Fans should be confident and comfortable with the club's long-term stability.
"The club needs them to survive like any business does and we are absolutely hoping they will stand behind and support the club the way they have in recent seasons. In the vast majority of areas, I think we are moving in the right direction and it is business as usual at the football club.
"The fans are looking for a degree of confidence that their club is stable, it's being properly run and we are in a good position financially. We are now in our best position financially in my time at the club so that's positive and we are placed very well for the start of the forthcoming Championship campaign."
Season ticket sales to the general public begin today and Wallace has asked fans to "put the in-fighting and the turmoil to one side" by again giving the financial backing needed for a push for promotion to the SPFL Premiership.
"For the club to thrive, it needs the support of its fans in order to have the financial base required to build and grow," he added. "There are many non-Rangers fans who support other clubs and who are genuinely concerned about the progress we are making.
"They know where we're headed and they would just love for us to falter. We're not going to allow that to happen. We have a tremendous opportunity now to come together as a club and a fanbase and unite to take us back to the top. Let's not waste it. This is our time to put the in-fighting and the turmoil to one side, to unite across the club and back the club."
Wallace also felt the club had taken "significant strides" since his appointment as chief executive at the end of last year, but warned that there was still much to be done.
"I've been in position now for a little over six months and in that time it has been extremely challenging," he added. "There have been so many legacy issues we have had to deal with and we spent a considerable period of time looking at the state of the business. We had to map out what we think the club and the business is capable of doing over the next several years.
"We have done a tremendous amount of groundwork and we've addressed a significant number of issues. In April, we published our business review. That gave fans a sense of what we inherited but more importantly, a sense of the vision of where we think we can take the business. We have made significant strides but it's not an overnight journey and what we are looking for now is to move forward again."
Wallace was joined in Toronto by former player Willie Henderson, as well as first-team squad members Steven Smith, Fraser Aird, Nicky Clark, Lee McCulloch, Luca Gasparotto and Lewis Macleod. Macleod has not featured for the Rangers first team since January after being struck down with a mystery virus which sparked worries that his career could be in jeopardy.
The Scotland under-21 midfielder, however, has been working intensely with physio Steve Walker over the past month and believes he is on schedule to rejoin the rest of the squad for pre-season training.
"I've been doing lots of running and weights and I've just been trying to get myself back to full fitness," he said. "I'm still a wee bit off yet but come pre-season I'll be ready to go and I'm looking forward to that.
"I was always hoping to be there or thereabouts by the time the players came back for the start of pre-season. With the way it's going, I should be close to full fitness when they come back and all being well, I'll be fighting fit and there will be no hiccups now."
Clark, meanwhile, has welcomed the return of Kenny Miller to the club, even if it might diminish his own prospects of regular football next season. Miller became manager Ally McCoist's first signing of the summer when he agreed a one-year contract last week and Clark hopes to benefit from the 34-year-old's experience. "Kenny's someone I can only learn from. I'm sure I'll take a lot from him," said the former Queen of the South striker.
"I've heard a lot about him from the boys who have played with him before and he's a really good player and a good guy. It'll be a good challenge for me. Every good team needs competition for places and the manager has brought Kenny in."