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".
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:
A West Yorkshire MP has demanded a "proper investigation" into a Cabinet Minster's outburst at police officers in Downing Street.
Chief Whip Andrew Mitchell has faced calls to resign after shouting at the officers when they refused to let him take his bicycle through the main gates.
Mr Mitchell has since apologised for not treating officers with due respect. He has denied reports he called them "plebs".
Yvette Cooper, the MP for Normanton, Pontefract and Castleford, has written to the Cabinet Secretary to request an investigation. She has also called on Downing Street to release a full account of what was said.