Smith spoke out after revealing his own consortium has withdrawn its £6m bid for the club after failing to receive information about Green's investors, how much working capital they have, or the business plan.
King expressed his own strongly-worded criticisms after a second meeting in 24 hours with the Rangers chief executive.
Smith's consortium, which is backed by Jim McColl, one of Scotland's wealthiest individuals, and Douglas Park, the transport tycoon, formally withdrew their offer yesterday.
The £6m bid was lodged with Zeus Capital, the investment fund that Green fronts, last Monday and despite repeated statements from Green, Malcolm Murray, Brian Stockbridge and Imran Ahmed, the board members, that Zeus have no intention to sell, they returned to the consortium with a counter-offer.
This was a ploy that Smith, McColl and Park refused to consider, since they have received no comfort about who has funded Zeus Capital's take-over, how much short-term capital they have raised and how they plan to take the business forward.
Green and others have repeatedly denied that Malcolm McDonald, the former Sheffield United chairman, and Rafat Rizvi, a British citizen who was once on Interpol's wanted list after being accused of stealing assets from Indonesia's Bank Century two years ago, are among the investors, even though the Evening Times understands that both men were enthusiastically and regularly discussing their involvement in the days and weeks running up to last Thursday's purchase of the assets from The Rangers Football Club plc.
Smith said: "I would like to clarify the background to the offer of £6m for the assets of the club which I announced on Thursday June 14. The offer was made to the administrators before the Charles Green consortium had concluded their transaction to acquire the assets at £5.5m from the administrators.
"We felt it necessary to have a fall-back position to secure the club's future.
"We have since made the same offer of £6m to the Green consortium through Zeus Capital.
"Our offer has been rejected and they have made a counter-offer inviting us to join their consortium.
"However, the current business plan is not in accord with our understanding of the present circumstances of the club and the way forward.
"We would prefer to leave them to proceed in their own way and we wish them good luck in their endeavours.
"Members of our consortium had met with Charles Green and Zeus Capital prior to [last Thursday's] CVA meeting and it had been agreed that we would be provided with significant information which would give us comfort as to the identity of the consortium members, their strategy and their funding capacity.
"This information had not been forthcoming by the date of our offer. We are therefore withdrawing completely from the process to enable Charles Green and his consortium to move forward.
"We very much hope the verbal assurances they provided to us – and the public statements made – are adhered to and that the club will therefore be financed and managed with appropriate governance and can go forward in a sustainable manner."
Green had pledged to raise £30m by the end of July, but there are now serious concerns about the group's ability to meet this month's working capital commitments, with the wages to be paid on June 26.
The Evening Times believes that Green's Sevco consortium has lost one of its backers.
Although he pledged to name all investors on the day of the asset sale, Green's group has only named a small number, one of whom – Ian Hart – immediately refuted that and declared himself a financial supporter of Park and McColl.
In a statement released yesterday, Malcolm Murray also said that Green's consortium had spoken to the Rangers Fans Fighting Fund (RFFF), and that they agreed with his call for the club to move forward.
However, members of the RFFF were angry at being used to lend newco Rangers credibility, since they are not due to meet Green and Murray until today. It is thought Murray later agreed to reword the statement.
Season ticket sales continue to be slow, with many fans uncertain about the intentions of Green's consortium, while sponsors are also pulling out.
King said in an interview with the BBC that he believes Green's plan is to profit from Rangers rather than rebuild the club.
KING, who is not planning to invest in the new regime, said: "Charles Green is the only game in town.
"The club needs money and I really don't know how he's going to find it.
"I've looked at the business plan and he's going to run the club to make a profit. I don't think that's possible.
"I believe for Rangers to be the Rangers we all want it to be, it requires investors to subsidise losses for a number of years.
"The only way to make money is to aggressively cut costs, so Rangers will survive but it won't be the Rangers in three years that it could be. It's a lot of money from investors that are not yet in place. He owns the club but doesn't have any money."
The Evening Times also understands that no Rangers players have received any contact from Green, even although the club is duty bound to set a date for the transfer of their contracts, and so allow them the opportunity to refuse.
There has also been no contact with the Professional Footballers' Association Scotland.
Murray said in his statement: "I am not in this for personal gain and what is of paramount importance is the club regains stability both in financial and footballing terms.
"We can say to supporters that the assurances the Walter Smith consortium are looking for regarding financial probity and high standards of corporate governance will be met.
"The board would urge all Rangers fans to now get behind the club."