The Labour Party MP, Kelvin Davis, says arming police could put officers' lives in even more danger.
The Police Association said that at its annual conference this week members unanimously voted for sworn officers to carry guns.
But Police Commissioner Mike Bush has said that will not be happening.
Labour's Kelvin Davis said arming officers would change the way they interacted with communities, and such a move was not justified.
"If anything, it might even put police lives in even more danger. As someone with a brother in the police force, I'm acutely aware of the need to balance the safety of both the police and the public."
Mr Davis said an unarmed force highlighted the trust the police and public had for each other.