The government will not extend the remit of its inquiry into the sub-postmasters scandal.
Business Minister Paul Scully rejected such calls saying it is important the inquiry reaches a swift conclusion.
He believes the current inquiry will deliver that more rapidly than would starting a new statutory inquiry.
In a long-running scandal, more than 700 people were wrongly convicted of offences of theft, fraud and false accounting.
As a result of prosecutions between 200 and 2014, some were imprisoned.
The government has launched an inquiry into the prosecution of the former Post Office workers.
But those affected have long called for a judge-led, full, public inquiry, rather than the government’s own inquiry which is set to report in the summer.
The current one cannot compel witnesses to attend or hand over evidence.
On Friday, 39 of the former Post Office workers saw their criminal convictions overturned by the Court of Appeal.
Other appeals are expected to follow in what is the most widespread miscarriage of justice in the UK’s history.
The convictions had been based on a flawed computer software system, called Horizon, which showed shortfalls in the sub-postmasters’ accounts which did not exist. The IT system was installed in 1999 under former chief executive John Roberts.
As the government is the only shareholder in the Post Office, Mr Scully also confirmed that the government will step in to cover financial compensation to more than two thousand individuals who have come forward to the Post Office having lost money because of the technical flaws in Horizon.
He stated that those payments have now begun to be issued.
A number of MPs also raised the question as to why the government had not apologised to former sub-postmasters for its lack of oversight during this period, and it’s financial backing of the Post Office as it spent £100m in legal fees convicting sub-postmasters through many years.
On Monday, the former chief executive of the Post Office, Paula Vennells, quit her roles on the boards of Morrisons and Dunelm following the IT scandal which led to the wrongful convictions of former postmasters. She was chief executive of the Post Office between 2012 and 2019.
Morrisons announced Ms Vennells would leave after serving as a non-executive director since 2016. She also said she would stop performing her duties as an ordained Church of England minister.
Ms Vennells said: “I am truly sorry for the suffering caused to the 39 sub-postmasters as a result of their convictions which were overturned last week.