Officials said the inmates had escaped through the tunnel, dug from a house to the wing of the prison where political prisoners are detained in Kandahar.
In an email, Zabiullah Mujahid, a Taliban spokesman, said the tunnel was 1,050ft (320m) long and had taken five months to construct, "bypassing enemy check-posts and Kandahar-Kabul main highway leading directly to the political prison".
He said just three insurgents inside the prison had known about the plot. They helped ferry the prisoners out of the jail in an operation lasting four and a half hours.
He said that by 3.30am on Monday morning, the entire political wing of the prison was emptied of inmates. These had been ferried off to "secure destinations" by a fleet of cars the Taliban had organised.
The message, written in near-perfect English, crowed over the failures of the security forces: "The most astonishing thing throughout the operation, as reported by mujahideen informants, was that all the enemy forces inside the prison, which includes foreign invaders, did not notice the results of the operation even four hours later and hence has not released any statements.
"Mujahideen had also placed a martyrdom-seeking group near the prison, whose need did not arise due to the inaction shown by the enemy."
Amir Muhammad Jamshad, the head of Kandahar's prisons, told the Guardian the tunnel was a major undertaking by the insurgents, who were unable to use any heavy machinery because it could have attracted attention to their work.
A man who Taliban spokesmen said was one of the inmates who helped organise the escape from the inside told the Associated Press a group of inmates obtained copies of the keys to the cells ahead of time.
"There were four or five of us who knew that our friends were digging a tunnel from the outside," said Mohammad Abdullah, who said he had been in Sarposa prison for two years after being captured in nearby Zhari district with a stockpile of weapons. "Some of our friends helped us by providing copies of the keys. When the time came at night, we managed to open the doors for friends who were in other rooms."
He said they woke the inmates up four or five at a time to get them out quietly. Abdullah spoke by phone on a number supplied by a Taliban spokesman. His account could not be immediately verified.
There are guard towers at each corner of the prison compound, which is illuminated at night and protected by a ring of concrete barriers topped with razor wire. The entrance can only be reached by passing through multiple checkpoints and gates.
Tooryalai Wesa, the governor of Kandahar, said that security forces at the prison had "failed in their duty", but strenuous efforts were already under way to recapture the prisoners.
"Some of the escaped prisoners have been recaptured by the security forces during searching operations, and huge operations have launched inside and on outskirts of Kandahar city for the rest of them," he said.
He also appealed to Kandahar residents to phone in tipoffs about the escaped prisoners to a special hotline set up by authorities.
Despite his insistence that the job of recapturing so many prisoners would be made easier by the detailed biometric records held on all the men, including fingerprints and iris scans, the breakout is a blow to international and Afghan government efforts in the key province.
One member of Kandahar's provincial council, Hajji Hematullah, said that although some prisoners may still be in the city, many others would have made a direct line for the safety of the Pakistani border.
The freeing of so many hardened insurgents comes just before the summer "fighting season", and could potentially reverse some of the gains Nato made over the winter in intensified operations aimed at killing and capturing as many insurgents as possible.
It is also the second time huge numbers of prisoners have managed to escape the prison in just three years. In June 2008, the Taliban stormed the prison, using a suicide bomber to break a hole in a prison wall. The operation allowed 870 inmates, including 390 insurgents, to escape.
The breakout was followed by days of intense fighting in the outskirts of the city after the insurgents fled to areas where they were immediately able to take up arms against Nato forces.
The crumbling prison was extensively reformed and improved in an effort to prevent such an outbreak ever happening again.