The South African-based businessman is expected to fly to Scotland later next week for a meeting with fans but now Somers wants a showdown too.
King stepped up his bid for boardroom change last Wednesday when he encouraged the Light Blues support to withhold season-ticket cash.
He then followed that up on Saturday with another press release accusing Ibrox chief executive Graham Wallace of insulting the Gers faithful.
The 58-year-old intervened after the club were forced to accept a £1.5million loan from investors Sandy Easdale and Laxey Partners.
The loan is secured against the club's Edminston House and Albion car park facilities, while Laxey stand to make a £150,000 profit in either cash or shares by the time their £1million is repaid according to terms criticised as wildly generous by supporters group the Union of Fans.
The ruling regime responded to King's 1,500-word statement by accusing him of "destabilising and damaging" the club.
Now Somers has written to King demanding a meeting.
His letter says: "The Board of Rangers International Football Club has noted your astonishing press releases over the past few days.
"These statements and innuendos are very damaging to the Club, which we can only assume is your intention.
"We wish you to attend a meeting to explain your allegations in more detail as soon as possible. Please confirm your availability."
Somers' letter was released to the media just hours after it was reported King's belief that the club will not call in administrators any time soon.
Rumours swept across social networking websites on Sunday night claiming Ibrox chief executive Graham Wallace was preparing the club for their second insolvency event in the space of two years.
The club responded by saying the rumours were "completely false" but the panic has worried already-anxious Gers supporters further following the £14.4million loss recorded last year.
However, despite vowing to take on the unpopular Ibrox board, South Africa-based King does not think the current directors are desperate enough yet to place the club back into administration.
The Castlemilk-born multi-millionaire said: "I don't believe that it is likely that the club will go into administration at the present time."
King also says Rangers boss Ally McCoist is right to take a step back from the Ibrox power struggle.
The feuding between King and the board put McCoist in an impossible position when he was asked which side of the battle he backed at his Friday press conference.
Instead of answering, though, the manager of the League One leaders opted not to discuss the latest drama at all.
But King says McCoist is right to shy away from non-football matters while the fight for control of the club intensifies.
"I believe that it is the manager's job to focus on team affairs and to stay away from the corporate activities that he has no influence over," he said.
"I have not had discussions with Ally on my recent statements and I don't believe that it would be appropriate for me to do so.
"Ally has always demonstrated his loyalty to the club and will, no doubt, continue to put the club ahead of any individual."