The Welsh Health Secretary, along with his Scottish counterpart, say there's been a "lack of meaningful engagement" over Brexit between them and their UK Government counterparts.
The joint letter from Vaughan Gething AM and Jeane Freeman MSP focuses on the UK Government's EU Settlement Scheme.
The letter states: "earlier ministerial engagement would have provided a more timely opportunity to discuss and agree matters such as including family members in the [EU settlement scheme] while still in its planning stages."
The proposals lay out how the government wants to secure the rights of EU citizens and their families after Brexit.
The health secretaries of Scotland and Wales say the scheme will have a direct impact on staffing levels within their respective NHS services.
The Welsh Government says: "Both Health Secretaries believe including family members in the [EU settlement] scheme would potentially help remove some of the uncertainty for EU staff at this unsettling time. It would also send a clear signal of how much the contribution they make to health and social care services across the UK is valued."
The joint letter states: "We are therefore disappointed to hear that the Home Office is unable to agree to our request to include family members in the scheme. We reiterate our view that the scheme as currently proposed is much more likely to deter, rather than to encourage, our EU staff from taking this opportunity to clarify their immigration status ahead of the UK leaving the EU on 29 March 2019."
A Home Office Spokesperson said: “The EU Settlement Scheme will make it easy for EU citizens to get the status they need. In late August, we invited a small number of EU citizens to apply as part of the first testing phase to prove some of the functionality and processes.
“In order to ensure that the numbers of those involved in the testing remain controlled, family members of those applying during the private beta are not able to apply – unless they are themselves eligible through their employment with, or support from, the participating organisations.
“Family members of those granted status under the private beta can apply when the scheme is rolled out more widely.”