Speaking to ITV later, Lammy said he had been "reassured" that the two prisoners at large were not violent or sex offenders.
"I'm not going to give details of those cases, because these are operational decisions made by the police, and you'll understand if they're about to arrest somebody they don't want me to blow the cover," he added.
The subject of accidental releases gained attention after Hadush Kebatu, who was jailed after sexually assaulting a 14-year-old girl and a woman while living in an asylum hotel in Epping, was mistakenly freed.
Kebatu was re-arrested two days after his release and has now been deported to Ethiopia.
Shortly after Kebatu's release, news emerged of two other prisoners who had been released in error - William Smith, who later handed himself in, and Brahim Kaddour-Cherif, who was rearrested.
The cases led to the government implementing new security measures including a "clear checklist" for prison governors to follow when releasing prisoners.
The latest releases happened since 11 November, when Lammy gave a statement to the House of Commons, outlining the steps the government was taking to resolve the issue.
The number of prisoners who have been let out in error rose by 128% last year, increasing from 115 in 2023-2024 to 262 in the following year.
There were just over 57,000 releases of prisoners who had finished the custodial part of their sentences in England and Wales in 2024-25 - a rise of about 13% on the year before.
The figures on mistaken releases include cases where individuals were released either too early or too late.