The Home Office has confirmed the 14 men still on the run from an immigration detention centre have all been convicted of criminal offences.
Riot police were called to the centre after fires were started
The men were among 26 people who fled the Campsfield Detention Centre in Oxfordshire following a disturbance there on Saturday night.
A spokeswoman for the Home Office said they had all served their sentences and were awaiting deportation.
She said the most serious offence any of them had committed was robbery.
"All of the individuals are foreign national prisoners and we will be working with the police to recapture these individuals, concentrating on the most serious first," she added.
Superintendent Robin Rickard, who is in charge of the police search, said: "We have a substantial number of resources dedicated to the task and are doing all we can to locate the detainees as quickly as possible.
"I urge members of the public to contact us immediately should they see anyone they believe could be one of those involved."
Campsfield, at Kidlington in Oxford, was converted to a detention centre holding 200 male asylum seekers in 1993 and is run by the American company GEO.
No-one from the company was available for comment.
However, local Liberal Democrat MP Dr Evan Harris has called for action at the centre which has seen a series of disturbances, including a mass hunger strike last week.
Dr Harris said: "It is not surprising that seemingly indefinite detention without charge or without conviction leads to frustration, misery and potential unrest.
"It is disturbances rather than escapes that have been the main feature of Campsfield House's troubled past and local people will be concerned that detainees have escaped from what is supposed to be a secure establishment.
'Most of no risk'
"There will have to be an inquiry into how this happened and whether private companies with one eye on the profit margin are capable of running sensitive and difficult establishments like this."
Imam Sajid, a former chairman of the Joint Council for the Welfare of Immigrants, urged the escapees to give themselves up, but also called for a change to the way immigrants are treated.
He said: "The problem we have is these people feel they are treated like criminals when their crimes are simply fleeing their own country for whatever reason.
"The vast majority are no risk to the general public. In fact many feel instead of being under lock and key they should be allowed to contribute to society."