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An initial agreement on building a new hospital next to the Royal Infirmary at Little France was reached between the government and NHS Lothian in 2018 and a £45m contract was awarded for preparation work.
But in December last year ministers said they would not fund the project "now or in the foreseeable future" and they ordered NHS Lothian to review its eyecare provision and disperse services across the region.
The decision sparked a public outcry and cross-party calls for a rethink.
Last week the First Minister said if re-elected the SNP would “renew” Edinburgh’s Eye Pavilion.
And asked if that meant she would agree to fund a new hospital, said: "If that's what the health board comes up with in terms of the favoured option then yes that's what we will do. We are giving a commitment that we will fund the plan they put forward."
Now Lothian MSPs are calling for the health board to put forward the plans for the new hospital so a replacement can go ahead as quickly as possible.
Lothan Labour MSP Sarah Boyack said: “The First Minister’s comments provide a clear opportunity for NHS Lothian to submit a renewed proposal to build a new Eye Pavilion at Little France.
" It’s clear from the public outcry and the concerns of clinicians that it’s vital that we retain 24-hour emergency eye treatments in Edinburgh and support the growing number of residents in the south east of Scotland who need access to a centre of excellence in Edinburgh and the development of world leading research.”
Lothian Green MSP Alison Johnstone also urged the health board to put forward the plans.
“Given the widespread support for a replacement for the highly-regarded Eye Pavilion, it’s important that NHS Lothian resubmit their proposals.
"There is great concern that this centre of excellence will be replaced with a fragmented service that may prove difficult to reach for those who most need it.”
And Lothian Tory MSP Miles Briggs said a new hospital was essential.
"Given Ncola Sturgeon is saying if that's what they want they can have it, they should get back to working towards the new replacement hospital.
"If Nicola Sturgeon is going to fund the new hospital, then let's go for it."
The current Princess Alexandra Eye Pavilion on Chalmers Street, which opened in 1969, was deemed no longer fit for purpose seven years ago but the government was saying it wanted NHS Lothian to plan on retaining it.
Dr Hector Chawla, former director of the Eye Pavilion, told the Evening News last month that refurbishing the building would be a waste of money.
"I think the building is just clapped out," he said "The roof is leaking, the theatre roofs are leaking, the walls are cracked, the lifts don't work. It would be pointless spending any money on it."