The row over the emergency closure of 17 schools in Edinburgh because of safety concerns, which left more than 7,000 pupils unable to start the new term, has deepened after serious defects were also found at two secondary schools built under private finance schemes.

Urgent safety inspections discovered that brick walls at Gracemount and Craigmount high schools have the same faults that had already led to repairs at three primary schools in the city, Edinburgh council’s chief executive, Andrew Kerr, revealed on Monday.

Some 7,700 children and teenagers, including 2,100 high school pupils preparing for their national and higher exams in two weeks’ time, were told to stay at home on Friday for an undetermined period, causing chaos for parents and employers.

The council said on Monday evening that it had drawn up contingency plans to ensure all pupils could either return to their own or attend another school by Monday next week, with priority given to all those sitting exams.

All S4, S5 and S6 pupils at the three secondaries where only partial private finance work had been done – Firrhill, Drummond and Royal High – will be back at school on Wednesday. Edinburgh University said it had found 114 rooms across its campuses that could house 4,000 pupils by the end of this week.

Two of Scotland’s largest trade unions, the teachers’ body the Educational Institute of Scotland (EIS) and Unite, said the scandal raised wider questions about the safety of dozens of schools built under private finance initiatives (PFI) and public private partnership (PPP) programmes elsewhere in Scotland.

Company records show that Edinburgh Schools Partnership, the private consortium that built, runs and owns the 17 schools under a 30-year contract, made profits after tax of £3.4m in 2014 against a turnover of £10.4m. It made £1.9m on a turnover of £11m last year, and paid out nearly £1.9m in share dividends over those two years. It has £12m iin its cash reserves.

The EIS questioned how construction of the schools, which are about 10 years old and were all built under the same PPP1 contract, had been approved, resulting in the serious structural problems.

Larry Flanagan, the EIS general secretary, told BBC Radio Scotland: “We’ve been long-term critics of these initiatives, largely because the main contracts have been a huge drain on school budgets.

“We are concerned to find there are major structural difficulties. There is a question mark around building controls and how they are applied. One question is about value for money in terms of how the work was done initially and then an ongoing question of the drain on budgets.”

Mary Alexander, the deputy Scottish secretary for Unite, said: “This is also not a situation exclusive to Edinburgh but one with national implications. The real question is how many other schools and infrastructure across Scotland built through PPP/PFI are affected, which means nothing other than a full review is required.”

The row erupted late on Friday after Edinburgh council disclosed that it was temporarily closing 10 primaries, five secondaries and two additional support needs schools – all built by ESP – just as pupils prepared to return after the Easter break.

The alert was raised after ESP carried out inspections on all 17 sites, as well as a community centre that has also since been shut as a precaution, after a wall collapsed at Oxgangs primary following a heavy storm in January.

They discovered that crucial fixtures called header ties, which bind the top of brick walls to a building’s main structural wall, were missing at several of those schools.

Councils across Scotland with PFI schools from the same era or the same construction firms carried out their own urgent inspections, but no similar problems have yet emerged.

Kerr confirmed at the weekend the council is likely to pursue damages and costs with ESP, which has acknowledged it “will accept full financial responsibility for investigating and resolving these issues”.