The Defence Committee has criticised what it calls the "closed-minded" attitude to protecting Northern Ireland veterans by the Northern Ireland Office (NIO).
The comments relate to the ongoing consultation process over how to best implement parts of the Stormont House Agreement.
The proposal proving controversial is the creation of a new body to investigate outstanding Troubles-related deaths.
In June, the Defence Committee renewed calls for veterans and others facing investigations into Troubles-related fatalities to be protected by a Statute of Limitations, to end the "vicious cycle of investigation and re-investigation".
The Committee's submission of a Statute of Limitations to the public consultation would cover all Troubles-related incidents involving forces personnel up to the signing of the 1998 Belfast Agreement, accompanied with a truth recovery mechanism.
The Committee have now had a reply from the Northern Ireland Secretary and they say while she acknowledges the "current system of addressing the past is not working well for anyone", the committee claims her response favours investigations under a Historical Investigations Unit rather than a Statute of Limitations.
Responding to Mrs Bradley's letter, the Chairman of the Defence Committee, Dr Julian Lewis MP, said:
"The speed of this reply and the length of the Secretary of State’s letter suggest that its outcome has already been predetermined in favour of a cycle of further investigation and re-investigation.
"Unfortunately, the Secretary of State’s letter is unsatisfactory and seems to be an attempt by the NIO to shut down debate on this important topic.
"This is particularly evident in the closed-minded approach towards a Statute of Limitations, coupled with a truth recovery mechanism.
"This blanket rejection also ignores one of the cardinal points about this debate - namely, the impact of the Northern Ireland Sentences Act which ensures that anyone convicted of murder or manslaughter during the Troubles cannot serve more than two years of a life sentence.
"The Secretary of State’s approach is in stark contrast to the recent announcement by the Defence Secretary of the establishment of a dedicated team at the MoD to consider the issue of the legal protection that can be provided to serving and former service personnel."
The Committee says it will continue to focus on the issue as part of a broader inquiry.
Earlier this month, the Defence Secretary said he was "prepared to go to any lengths" to prevent what he calls a "vendetta against former service personnel", before setting up a team to look at proposals to protect armed forces veterans from prosecution for historic allegations.
Karen Bradley's office has been contacted for comment.