North Yorkshire County Council had raised concerns about Sustainability and Transformational Plans (STPs) which will become the funnel for funding health services.
The local authority said the plans could concentrate spending in more densely populated urban areas at the expense of meeting rural needs.
The council's Scrutiny of Health Committee had warned that the new plans could be unduly influenced by the challenges faced in providing services in the urban areas of Middlesbrough, Leeds, Bradford and Hull.
A government deadline of June 30 will now merely be for draft plans which "will form the basis for discussion".
Yorkshire's scrutiny committee said it welcomed the government's decision to give more time for plans to be finalised.
STPs form a key part of NHS planning guidance for the next five years, it said.
These place-based plans divide North Yorkshire's clinical commissioning groups into three urbanised regions for transforming the delivery of health care services.
The areas cover West Yorkshire; Durham, Darlington, Tees, Hambleton Richmond and Whitby; and the Humber Coast and Vale.
North Yorkshire's councillors had warned that STPs threatened to sideline the health needs of rural communities.
Scrutiny committee chairman Jim Clark said he remained "very concerned about the whole process" and the configuration of STPs.
But he added: "This new sense of realism should allow more time for local authorities, the voluntary sector, patients and the public to be more involved in the planning process.
Councillor Clark said this should form the basis for a full public consultation and allow us to turn this potential threat into an opportunity.
If done correctly, it could help improve all aspects of health and care across North Yorkshire.
It could also result in the development of new integrated models of primary care which would be "local to where people live".