Council bosses have called for a review of maternity provision in the wake of a report into acute services on Teesside.
The review looked at facilities at Hartlepool's hospital
An 11-month study recommended the creation of a centre of excellence in women's and children's services at Hartlepool's University Hospital.
But council bosses in neighbouring Stockton claim the move could affect an existing centre of excellence at the town's North Tees Hospital.
Stockton Council wants the report's authors to rethink the recommendations.
A campaign was mounted during the study, urging the retention of Hartlepool's main hospital, amid fears it would be closed in favour of a new £175m facility near Stockton.
But the inquiry, headed by Professor Ara Darzi, recommended the site remain, with the creation of additional centres of excellence.
Stockton says the recommendation to remove consultant-led maternity services for North Tees Hospital raises "grave concerns".
Council leader Bob Gibson said the decision was surprising when on average 2,000 babies are born in Stockton every year and only 1,000 in Hartlepool.
He has called for a special meeting of the authority to consider the report and discuss how to ensure Stockton's voice is heard.
He said: "There are excellent facilities at North Tees Hospital, and Stockton women should be able to continue to have their babies locally, knowing that a consultant-led service is available if they need it.
"There's never been an argument about Hartlepool hospital closing. This is a debate around the neo-natal facilities and where they should be placed.
"It will mean a lot of people travelling to Hartlepool from Stockton, when in fact, the best benefit for most people is to have it the other way about.
"The professor has got it the wrong way round in our view."