Private companies are better at running prisons than the public sector, a study by a centre-right think tank says.
Reform said 10 out of 12 privately-run prisons had lower reoffending rates among those serving 12 months or more than comparable public jails.
Last year, the government signalled a move away from wholesale privatisation in England and Wales. Reform says this decision is not backed up by evidence.
Justice Minister Jeremy Wright said the report was a "simplistic analysis".
Privately-managed prisons were introduced in the UK in the 1990s and there are currently 14 private prisons in England and Wales, all managed by one of three firms - G4S, Serco and Sodexo Justice Services (formerly Kalyx).
Value for money
In November, Justice Secretary Chris Grayling set out the government's plan for prison competition and he decided four prisons, including G4S-run HMP Wolds, should be run by the public sector.
Mr Grayling said private firms would be brought in to all public prisons to run maintenance, resettlement and catering, saving up to £450m over six years.
Policy groups, including Reform, said the decision amounted to the end of competition for prison management between the public and private sector, although Mr Grayling insisted it did not rule out further prison-by-prison competitions in the future.
For its report "The case for private prisons", Reform studied Ministry of Justice statistics for prison operation performance and rehabilitation. Some data was not available for all of the 14 private prisons.
The think tank said private prisons outperformed their public counterparts in the majority of the performance measures used by the Ministry of Justice.
Among the report findings were:
- seven out of 10 privately-managed prisons had lower re-offending rates among offenders serving fewer than 12 months
- 12 out of 12 private jails performed better than the public sector at "resource management and operational effectiveness"
- However, seven out of 12 public prisons performed better than private jails at "public protection"
Report author Will Tanner said: "Private contractors outperform comparable public sector prisons on both cost and quality, delivering better value for money for the taxpayer.
"In addition, the vast majority of contracted prisons have lower reoffending rates than similar public sector prisons for both long and short term prisoners, a key government objective."
Reform recommended that all prisons should be subject to competition. It also called for the end to national pay bargaining for prison officers with pay and conditions to be set locally by governors.
Serco and G4S were among 64 firms which provided more than £5,000 in sponsorship for events run by Reform last year, but the think tank said it was "editorially independent" .
Mr Tanner said its external reviewers included former governors of public sector and private sector jails. He added that the data on which its analysis was based was from the government, not the private sector.
Justice Minister Jeremy Wright says Reform's "simplistic analysis does not tell the whole story".
"A wide range of factors contribute to reoffending including previous criminal behaviour, drug and alcohol dependency and the support offenders receive on release from prison," he said.
"This is why we are committed to introducing significant reforms that will bring down our stubbornly high reoffending rates."
Juliet Lyon, director of the Prison Reform Trust, said the report's selective use of data masked "decidedly mixed results".
"Some private prisons have proved innovative and effective, but others have been criticised by the Chief Inspector for their high staff turnover, tendency to cut corners and weaknesses in security.
"From Ministry of Justice data, it is almost impossible to compare the performance and reoffending rates of one establishment with another, partly because prisons hold different categories of offenders and also because prisoners often serve their sentences in a number of different jails."
And Steve Gillan, of the Prison Officers Association told BBC Radio 4's Today programme his trade union was opposed to private prisons in concept and because it believes "it is a duty of the state" to handle justice and not for share holders who would be "gaining from incarceration".
However, Jerry Petherick, G4S managing director of custodial and detention services, said the report had looked at a "wide range" of official performance measures.
"This report acknowledges that the private sector is a source of innovation in areas like reducing reoffending, encouraging employment and fostering an environment which promotes constructive staff-prisoner relationships," he said.