A West Yorkshire MP has said the Prime Minister needs to "show some leadership and judgment" over the Andrew Mitchell incident.
Yvette Cooper, Labour's Shadow Home Secretary, said David Cameron should make Mr Mitchell stand down as Chief Whip "straight away".
It follows claims he called police officers "plebs" after they made him wheel his bike out of Downing Street's pedestrian exit instead of opening the main gate.
He has apologised to the officers but has denied using the word "plebs".
Defence Secretary Phillip Hammond said the row had been "hijacked".
We urged David Cameron and Andrew Mitchell to properly deal with this incident from the start. Instead the drawn out saga of half apology and oblique denial has left a cloud hanging over the Government's attitude to public servants.
It is now very hard for the Chief Whip to command respect in Parliament or beyond.
The Prime Minister needs now to show some leadership and judgement and take seriously the message this incident has sent to people across the country about his Government. He needs to end this now and make Andrew Mitchell stand down as Chief Whip straight away.
– Yvette Cooper MP (Labour, Normanton, Pontefract and Castleford)
Downing Street says no investigation will be carried out into the conduct of Chief Whip Andrew Mitchell.
It follows a letter requesting such an investigation from Yvette Cooper, the MP for Normanton, Pontefract and Castleford.
There were calls for Andrew Mitchell to resign after shouting at police officers when they refused to let him take his bicycle through the main gates at Downing Street. He has since apologised for his behaviour, but denies reports he called them "plebs".
The Secretary of the Cabinet, Sir Jeremy Heywood, has responded saying:
In light of the apology given, and also the fact that the officer concerned has accepted the apology and does not want to pursue the matter further, the Metropolitan Police Commissioner reiterated that no further action would be taken.
Given these circumstances neither the Prime Minister nor I see any purpose in a further investigation. The Prime Minister has already made clear that he regards Andrew Mitchell's behaviour on this occasion as falling well short of the standards expected of members of the Government.