Andrew Burns of Edinburgh City Council said Scottish and UK ministers should examine the findings of the inquiry, led by construction expert John Cole, when they are published in December.
By the start of term last week, children and young people had returned to all the schools affected in April after the collapse of a wall at Oxgangs Primary. About 7,500 pupils and more than 600 staff from nurseries, primaries, secondaries and special schools had to be moved pending safety inspections and repairs.
The Labour councillor denied opposition claims that funding the schools in a public-private partnership (PPP) had played any part in the defects. He cited similar defects in wall and header ties – which bind brick walls to the main structure – in other buildings that were constructed under traditional procurement, including Lourdes Primary in Glasgow.
“I think this is more of a construction issue, which is why John Cole’s independent investigation in Edinburgh, I think, will have implications much wider beyond Edinburgh – probably for the whole of Scotland and the rest of the UK,” Mr Burns said.
“There were schools closed in other parts of the country, particularly in Glasgow where Lourdes Primary shut after four years of being opened, which was built under traditional procurement, so it’s not as clear cut as the type of finance.”
Miller Construction, which was bought by Galliford Try in 2014, built the Edinburgh schools, with maintenance provided by the Edinburgh Schools Partnership (ESP) and partner Amey BPO Services.
Mr Burns said the council would “absolutely” be able to hold private companies accountable for the defects, which have already cost ESP many millions of pounds in withheld council payments.
He told BBC Radio Scotland: “We have been withholding that unitary charge for several months now, and we are talking several million pounds over the course of May to August while the schools have not been available, so there has been no cost to date to the local authority.
There has been significant expenses in arranging buses for pupils around the city, but that has all been deducted, in effect, from the unitary charge.”
There were no indications exam results had been affected by the disruption, he added.
Meanwhile, a trade union coalition has urged Scottish first minister Nicola Sturgeon to hold a Scotland-wide inquiry into PPP.
Signatories include the Scottish Trades Union Congress (STUC), Unite, Unison Scotland, NASUWT, the general secretary of the Educational Institute of Scotland, Larry Flanagan, and the Common Weal think-tank.
Mr Flanagan said PPP levied “on-going exorbitant costs to the public purse, when all available money should be channelled into supporting already stretched services”.
Dave Watson, head of policy at Unison Scotland, said a wider inquiry should look at the prospects for ending existing contracts using low public sector borrowing costs. Joel Benjamin, campaigner for the UK-wide campaign group People vs PFI, said: “Scotland has 40 per cent of UK PFI schools, with just 8.5 per cent of the UK population.”
Pat Rafferty, Unite’s Scottish secretary, said: “We need our MSPs to seriously consider the option of cancelling or renegotiating unfair and extortionate PFI contracts, and we need to make sure that the private finance alternatives put forward by the Scottish government will really deliver value for money.”