Six cameras and a mobile detection unit were brought in at the beginning of June to catch drivers illegally using the bus lanes.
The vast majority of erroneous ones are from the cameras in Donegall Square East.
Incorrect penalty charge notices will be cancelled and refunds provided.
Transport Minister Danny Kennedy said: "To find out that there has been a fault with the system is unacceptable."
"This mistake will not impact the scheme.
"The ambition of the scheme is not to raise money, but to keep the traffic in Belfast moving." he added.
More than 6000 tickets have been issued in total since the scheme began.
Money raised from fines goes towards an audio visual scheme on buses, to help the visually impaired and hard of hearing.
NSL, the company that operates the scheme on behalf of the Department for Regional Development, said the error "was a time-based one, in which camera processor timing settings were incorrect".
An audit of log files between 22 June, when the first fines were imposed, and 21 July had found 118 penalty charge notices (PCNs) were issued in error, NSL said.
A further 612 fines given while the camera settings were incorrect were also cancelled, the company said.
"All those motorists affected have been identified and they should already have received - or will soon receive - a letter from Transport Northern Ireland to explain what has happened, to let them know that their PCN has been cancelled or refunded," a spokesperson said.
"We want to offer our sincere apologies for any distress this may have caused them.
"We have identified what went wrong with the system and have taken measures to ensure this does not happen again."
Mr Kennedy said he was setting up an independent technical audit of the arrangements for issuing the penalties.
An external review of the response to the problems, including the role of his department and NSL, would also take place, he said.
"I have sought and been given assurance by NSL and their contractors Zenco that this matter has now been thoroughly investigated and that the cause of the timing issue has been identified and resolved," he said.
"Going forward, NSL has given a strong assurance that there will be no further recurrences of the fault.
"NSL has put in place a number of measures, including checks on all video clips of potential contraventions to be carried out by both NSL and Zenco, and the provision of a daily status report to my department on the outcome of these checks."
The cameras use number-plate recognition technology, and it is anticipated that more than 10,000 drivers a year will be caught.
Penalties of Â£90 are reduced to Â£45 if paid within 14 days. Motorists who believe a penalty has been wrongly issued are able to appeal.
The fixed cameras are positioned at:
The mobile detection unit is monitoring main roads into the city including the Shore Road, Lisburn Road and Ormeau Road.
More than 700 fines handed to motorists using Belfast bus lanes have been cancelled because of a "timing issue" with detection cameras.