Ms Parkin's decision in effect meant the Green Party was dead, the Southwark and Bermondsey MP said.
He added: 'The Green Party have brought fundamental change to political thinking. But in the 1990s the really green party in British politics - the Liberal Democrats - are ready, willing and able to take up the mantle of the environmentalist force in British politics.'
Ms Parkin decided to quit her post after the decision by some members to invite David Icke, the former BBC Television presenter and self-styled prophet, to speak at next month's party conference.
Ms Parkin told the executive in a letter that she would not be standing for re-election to it at the Wolverhampton conference where she was due to face a barrage of motions reducing her power.
'I have been forced to the conclusion that the Green Party has become a liability to green politics,' her letter said.
Yesterday Ms Parkin told BBC Radio 4 that she and the whole executive had not felt it was in the party's interests to invite Mr Icke, the former national spokesman for the Greens, who last year declared himself the 'Son of God', to speak at the conference. 'But a small number of people are insisting that he be there,' she said.
Mr Icke, a former television sports presenter, shocked some party members with his announcement that he was on a mission to save the world.