The director general of the Prison Service has admitted that he does not know exactly how many inmates are on the run from open jails in England.
Mr Wheatley said most inmates who absconded were arrested promptly
Phil Wheatley said there was no central system in place to count people who had been recaptured after escaping, but such a database would now be developed.
The Conservatives said the lack of a central tally showed the "shambles" in the Prison Service had got worse.
The Liberal Democrats said it was a symptom of prison overcrowding.
Almost 700 inmates escaped in the year to last April from England's 15 open jails, Mr Wheatley estimated.
Earlier this week, the Home Office, replying to a Freedom of Information Act request, said 401 of the prisoners remained at large.
But the figures were compiled last May, and Mr Wheatley said he was "embarrassed" to admit he was unable to provide an accurate up-to-date figure because there was no central database for recording numbers of recaptured prisoners.
However, he could answer queries on a case-by-case basis, and overall the number absconding was dropping, he said.
He added that a central tally would be created in future, even though it would not help the service track missing prisoners any more efficiently.
"The crucial thing is that the police know who is unlawfully at large, and when they pick someone up know is that person unlawfully at large and can they be brought back into custody," he said.
"That the system does perfectly."
'Not rocket science'
Open prisons, or category D prisons, are often used to prepare low-risk inmates for release, and have a more relaxed security regime than others.
But Colin Moses, national chairman of the Prison Officers Association, said that because of prison overcrowding, prisoners were being reclassified as suitable for open conditions "far too quickly".
"We are seeing the wrong type of prisoner placed in category D conditions, so we are seeing an increase in the absconding rate," he told BBC Radio 4's PM programme.
He added: "We know on a daily basis how many people we are locking up, so surely we should know on a daily basis how many people abscond. This is not rocket science."
The Conservative Party's spokesman on prisons, Edward Garnier, accused Home Secretary John Reid of a "reckless disregard for public safety".
"It's an embarrassing shambles... it's a failure of planning, and it's a failure of management and it's a failure of producing a proper strategy which has led the government into this mess."
Liberal Democrat home affairs spokesman Nick Clegg said Mr Wheatley's admission was "yet another symptom of the government's self-inflicted overcrowding crisis in our prisons".
Total capacity of around 5,000
Houses secure jail transfers
Inmates categorised as low-risk
More relaxed security regime than other jails
"With chronically overcrowded prisons, it is inevitable that the wrong kind of offender ends up in open prisons and that the system simply struggles to keep a proper head count," he said.
But Juliet Lyon, director of the Prison Reform Trust, said open prisons were a vital part of the rehabilitation process of long-term offenders.
"Instead of panicking about absconds from open prisons... or berating the Prison Service which, despite gross overcrowding, has been able to reduce absconds and cut escapes from closed institutions, we should all demand to know what the home secretary is doing about appalling reconviction rates," she said.
She said those were running at over two in three of all released prisoners and well over three-quarters of young offenders.
Meanwhile, police hunting two convicted murderers who absconded from an open jail released photos of the pair.
Jason Croft, also known as Jason Fox, 28, from Salford and Michael Nixon, also 28, of Blackley, Manchester, left Sudbury Prison in Derbyshire last year.