A consultant engaged by the City in March had called for the demolition of the jetty.
Primarily used for fishing and not for mooring, the jetty was damaged in a severe storm in June 2012, and then closed.
An insurance claim for repair was refused on the basis that damage occurring through water from, or action by the sea, tidal wave or high water was a specific exclusion to the policy.
Council now wants to allocate $700,000 in the 2015/16 budget for a feasibility study of all maritime infrastructure at Wells Park.
This would include looking at the need for construction of a new jetty recreation facility at Wells Park and a review of the Wells Park Master Plan.
If a budget surplus occurs in the coming financial year then $300,000 could be prioritised to cover the demolition cost of the existing jetty remains.
The petition was presented on February 25 by Cr Dennis Wood on behalf of Wayne Steegstra.
Kwinana was represented by 675 signatures and a further 299 came from Rockingham, with much of the remainder spread across the south-west metropolitan area, including Mandurah.
Some signatures were even sourced from across the nation.
The original jetty was built between 1953 and 1965, extending from the wreck of the SS Kwinana.
The T-shaped head to the jetty was added in the mid-1970s and eventually the steel piles, steel crossheads and a new timber deck replaced the original structure.