Chief Minister John Le Fondré faces a battle to save his job on Tuesday, with States Members appearing split ahead of a crucial day in the Assembly.
Criticism has been levelled at both the Chief Minister and Mr Parker after the latter accepted a non-executive directorship with New River. Despite the Council of Ministers agreeing that the role was 'not compatible' with Mr Parker's role as Jersey's top civil servant, the chief executive did not give up his directorship.
And the Chief Minister is due to face a vote of no confidence partly due to his handling of the situation.
In a statement, Senator Le Fondré said: 'I have agreed with the chief executive that he should stand down from his role as chief executive and head of public service.
'Whilst the government has set out the draft Government Plan, setting a more certain future for the Island over some challenging years to come, we have found ourselves significantly distracted by an overt attempt to derail the progress that this government has made over the past two years and a challenge to our plan for the future.'
The Chief Minister paid tribute to Mr Parker adding: 'The progress we have made, and the plans set out ahead, have been steered by Charlie as chief executive and I would like to pay tribute to his determination on behalf of the government. However, his position has become a distraction from the government agenda, and he has agreed to stand aside.
Senator Le Fondré also said that Mr Parker's commitment to the Island has 'never been in doubt'.
Full story in Tuesday's JEP.