The women and equalities committee published its inquiry report in April, setting out recommendations to help improve outcomes in a range of policy areas, including health, education, hate crime and violence against women and girls.
However, the letter sent by the committee to communities minister Lord Bourne states that "some of the response lacks focus and specific commitments, and we have asked the minister to report back to us in 12 months' time".
A statement from the committee describes the letter, signed by chair Maria Miller, as setting out its "concerns that several key recommendations have been ignored".
Miller says: "These issues are not new.
"Gypsy, Roma and Traveller people have some of the worst outcomes of any ethnic group - in health, education and employment - and they face high levels of discrimination and hate crime."
The report called for increased powers for local authorities to inspect the quality of home education, after finding that GRT children could be missing out.
However, a government proposal to create a home schools register "does not go far enough" to address the challenges that GRT parents face.
"Children can be expected to become homemakers or go out to work as young as 11, and parents need better support to ensure a better future for their children," the letter states.
The committee also criticises the government for dismissing its call for all councils with Roma populations to consider selective licensing of private accommodation.
"The response that selective licensing areas cannot be designated on the basis of demographics or risk of exploitation misunderstands the evidence which led to this recommendation," it says in a statement.
It adds that the reasons Roma people were being exploited were explored by the evidence, and these are criteria which could qualify for licensing.
These included being recent migrants, having high levels of deprivation and tending to live in areas with poor housing conditions.
A further recommendation to make the pupil premium system work better for GRT children has also not been taken up by the minister, the letter claims.
"We recommended that the pupil premium process be sped up to ensure that Roma children who arrive in a school mid-year will be able to benefit from it," it states.
"You stated that the pupil premium allocation is allocated in line with the school census which is conducted annually.
"We recognise that this is currently the case but believe that the school census is therefore not an appropriate mechanism for ensuring that a school receives the funding it needs to support Roma and other pupils with support needs."
The committee has also asked Lord Bourne to provide further detail on the government's plans to increase the capacity of community organisations that work with schools to provide role models from GRT communities.
It also wants a review of the amendments to pupil registration regulations, due to be published in September, to engage with GRT issues to ensure that the problem of children missing from education is tackled effectively.
In addition, it says that data collection should be improved as GRT people were still unable to identify themselves to public services which could then not take their needs into account.