The hospital is at risk of losing its A&E and maternity services in a planned shake-up of Dorset's health services.
Dorset Clinical Commissioning Group (CCG) wants one hospital to specialise in emergency care for the county and its preferred site is at Bournemouth.
Borough of Poole councillors voted in favour of supporting Poole to become the county's main A&E department.
A clinical services review is proposing major changes at Dorset's three main hospitals, as well as across community care.
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A packed meeting on Tuesday heard that, under the plans, Poole would lose elements of its A&E, maternity and lead cancer care services, focussing instead on minor injuries and planned care such as operations.
Poole health councillor Karen Rampton said: "There's no dispute over the principal behind it, the hospital services need to be reconfigured - health are facing austerity measures just as we are in local government.
"We all support the principal of having a consultant led, 24/7 emergency care - it's just really the dispute over which hospital site is best to deliver that.
"We think it should be Poole because they are renowned for their cancer care, for their trauma, for their maternity in particular and we think they should maintain those services."
The results of a consultation into the review were published two weeks ago.
A final decision on the proposals will be made later this year.
Councillors have voted unanimously to fight the proposed closure of Poole Hospital's emergency care department.