Defender Tal Ben Haim and midfielder Liam Lawrence both need to depart the club before the August 10, otherwise the club will cease to exist before they even play their first game of the season - a League Cup tie against local rivals Plymouth.
Administrator Trevor Birch thanked Kitson and his agent for their approach to Pompey's plight, and wished the player the best for the future.
"I'd like to thank Dave and his agent for the stance they've taken to give Portsmouth Football Club the best possible chance of survival," Birch told Portsmouth's official website.
"We thank Dave for his service to the club and wish him every success for the future."
The South Coast club's fall from grace since their 2008 FA Cup triumph has been spectacular, with two relegations in three years leaving the former Premier League club with an unsustainable wage bill - and battling creditors on all fronts.