G4S, the company at the centre of the Olympic security fiasco, has started to recruit staff to carry out criminal investigations for a police force, with duties that include house-to-house inquiries, giving evidence in court and undertaking "sensitive high-profile cases under limited supervision".

The news comes as two Cabinet ministers said the G4S failings at the Olympics had caused them to think again about how private contractors should be used.

The G4S adverts for "civilian investigators" to work on long-term "open-ended" contracts based in local investigation units throughout the Warwickshire police force first appeared last Wednesday on the G4S Policing Solutions website. They appear to push new boundaries in the debate over police privatisation during which ministers have said that "core policing" tasks will not be put out to tender.

G4S boss Nick Buckles last month accepted when questioned by MPs that the company's failure to produce enough staff for the Olympics had been a "humiliating shambles". On Tuesday cabinet ministers Philip Hammond and Jeremy Hunt said that the outcome of the £284m G4S Olympic security contract had caused them both to "think again" about the default use of private contractors.

The Police Federation said it hoped the home secretary, Theresa May, would "take credence of this move" to recruit in Warwickshire and ensure that domestic security was undertaken by public servants who were fully trained and accountable for their actions.

Warwickshire police confirmed the move, saying they needed to recruit additional staff "from time to time" to meet specific operational needs and that recruiting them on a contract basis gave the force flexibility.

"The requirements of the work we are currently recruiting for requires specialist investigative skills, but does not require the full warranted powers of a police officer," said a Warwickshire police spokeswoman.

Recent Home Office figures show that Warwickshire police have lost more officers than any other force bar one, despite being the smallest in England and Wales with only 802 officers remaining, down from 1,000 in 2008. The force needs to find £10m of further savings by 2015.

The G4S advert says the civilian investigators to be based in Nuneaton, Rugby and Leamington will investigate crime, gather evidence, seize and view evidential material, take statements from victims and witnesses, undertake house-to-house inquiries, prepare files for the Crown Prosecution Services, attend court hearings and give evidence, and identify and trace offenders.

It says the jobs would be "ideally suited to experienced ex-police" and successful applicants would be required to "undertake sensitive high-profile case inquiries, be able to carry out any role within a major incident room, and have specialist knowledge on all aspects of crime investigation".

James Plaskitt, the Labour candidate for police and crime commissioner in Warwickshire, said: "Anyone reading that job description would think it was the definition of a police officer's work. Well, it is. It suggests to me that we have indeed lost too many officers in Warwickshire as a result of government-imposed cuts, and now the force is turning to G4S to plug the gaps."

He added: "If we need people to work on 'sensitive high-profile cases' I would rather have the reassurance that these are fully integrated police officers, not staff answerable to G4S. Policing should be for public protection, not for profit."

Despite the fact that the advert says that G4S Policing Solutions is "currently recruiting" for the posts and invites applicants to email the company, Warwickshire police said G4S was only acting as an agency site.

"Warwickshire police has a contract with the national recruitment agency Reed who in turn advertise on a number of agency sites, including G4S. Staff employed on a temporary basis are contracted to Warwickshire police by Reed, and will be vetted by the force in respect of their suitability. They will be answerable to the force in respect of their work," said its statement. The jobs did not appear to be advertised on the Reed website.

"Warwickshire police is currently recruiting investigative staff in order to continue to focus on those criminals who commit acquisitive crime, which includes house burglary, car crime and robbery," the force added.