Building work on community health centres in Firrhill and Muirhouse has been put on hold because of new European Union rules.
The news comes after education leaders in Midlothian admitted construction of a replacement Newbattle High School had also been postponed due to the change.
Signed off under the Scottish Futures Trust (SFT), the projects were previously treated as private sector based.
But updated regulations mean they may now be classed under the public sector heading, leading to a potentially significant impact on budgets and forcing detailed contract reviews.
It is not known how long the freeze will last, although sources at the Scottish Government have indicated they expect delays to be “small”.
But angry community leaders said there was deep frustration that construction of the clinics in Firrhill and Muirhouse – originally scheduled to begin on site over a month ago – had yet to commence.
The centres were supposed to be up and running in 2011 but funding changes affecting the city council and NHS Lothian saw the plans put on ice.
Heather Levy, chair at Firrhill community council, said: “We’ve been lobbying for this new medical centre for what feels like decades.
“We’re the only area in Edinburgh that does not have this service, as far as I’m aware. I hope it’s only temporary or you’ll see us jumping up and down with more than just frustration.”
Robert Pearson, chair of Tenants and Residents in Muirhouse, said: “Already, we’ve started to be inconvenienced – utilities have been diverted and Muirhouse Avenue has been closed completely.
“What the government is saying [about short delays] is no reassurance whatsoever. They need to come forward and say if it’s likely to be [a certain number of] weeks or months.”
A Scottish Government spokeswoman said: “There has been some movement in the scheduled dates for reaching financial close and commencing construction, but this is being mitigated by close liaison between SFT and project partners, to enable rapid steps to be taken to bring projects to financial close when that is possible.”
Iain Graham, director of Capital Planning and Projects at NHS Lothian, said: “We are working closely with our council partners, Hub South East Scotland and Scottish Futures Trust to resolve final outstanding points and ensure that the projects can continue as planned without extensive delay.”
Councillor Ricky Henderson, health and social care leader, said he was “committed” to improving services across Edinburgh.