Under the first phase of the early release scheme, offenders serving sentences of up to 19 months were eligible to be released after serving one third of their sentence.
The move, which will see a further 2,500 prisoners released across the country by the end of the year, is due to the prison system running on 98.2% capacity.
The MOJ said: “We will never jeopardise public safety. That is why we are putting thousands more Neighbourhood Police officers on to our streets, upping police funding to £18.5bn and taking investment in the probation service to record levels.
“To manage offenders out on licence, we are rolling out the toughest-ever controls, including world-first restriction zones, the largest expansion of electronic tagging, and giving victims a say in licence conditions.”
GMP Deputy Chief Constable Terry Wood said the force had been working “closely” with partners so that “robust plans are in place to ensure offenders are adhering to their conditions” adding that any breaches “will be, and are being – enforced by GMP”.
“As with any offending in Greater Manchester, where there is a report of a crime we will respond promptly to take positive action to protect victims and pursue criminals,” he added.