In a statement, East Lothian Council said the parties involved needed to "make clear their intentions" for the future of the facility as it prepares a detailed plan for development in the region.
Ms Leitch said: "Now that our Main Issues Report consultation has closed we must move towards major decisions in the preparation of our proposed Local Development Plan. It is very difficult for us to strategically plan in land use and economic development terms with the current ambiguity.
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"As site owners, ScottishPower has a critical role in determining the future of this location. It also has a planning approval to develop a high efficiency gas power station on the land. However it has not confirmed if it intends to continue with this development.
"The council is coming under pressure to develop a masterplan for the area. With no clear picture coming forward it would be imprudent to commit substantial public funds – and raise public expectations – creating a vision for land which is in private ownership.
"We are also seeking clarity from Scottish Enterprise on its proposals for the site which have caused concern across the community. We are therefore seeking a meeting with relevant parties to obtain clarity for the council and our community."
Cockenzie Power Station stopped production in March 2013. The site has since lain empty, with a phased project to safely demolish its structure being undertaken in recent months.
(JP/MH)
