Scotland’s public services are facing more crippling strikes after teachers and nurses announced they would be going on strike over pay.

The country’s largest teaching union, the EIS, said its members overwhelmingly rejected a 5% pay offer and repeated its claim for a 10% rise.

The EIS said 96% of its members backed a strike on a 71% turnout. It insisted the government must come back with “a greatly improved pay offer if strike action starting this month is to be avoided.”

EIS general secretary Andrea Bradley said members had become “increasingly angry over their treatment” by their employers and the Scottish government.

She said: “Our members should have received a pay increase in April but, after months of unjustifiable dither and delay from Cosla and the Scottish government, we are still waiting for an acceptable offer to be made.

“Quite frankly, our members have had enough of waiting and enough of feeling the financial strain of the cost of living on top of the significant stress of their teaching jobs.”

Deputy First Minister John Swinney has said there is no more money to fund public sector pay rises.

Education Secretary Shirley-Anne Somerville said the Scottish government recognised “the vital importance of reaching a fair and affordable resolution on pay.

“Strikes in our schools are in no-one’s interest,” she said, “least of all for pupils, parents and carers who have already faced significant disruption over the past three years.”

The EIS announcement came after Scotland’s largest nursing union voted for the first time to go on strike at all 23 trusts.

Members of the Royal College of Nursing (RCN) in Scotland have followed a number of other health unions in rejecting the Scottish government’s revised pay offer.

The RCN has said talks with health boards about deploying nurses in life-preserving services such as intensive care during any strike action are under way.

Humza Yousaf said the industrial action backed by the country’s largest nursing union was not inevitable and he wanted further talks on a new pay deal.

Mr Yousaf suggested there was scope to redistribute the existing £480m budget for NHS pay rises, but that no extra funding was available.

Strike action is expected to start by the end of the year.

Around 100,000 civil servants have also voted to strike over pay and conditions, the Public and Commercial Services Union has announced.

The threshold for strike action was met in 126 areas, from border force officials to driving test examiners.

The PCS is calling for a 10% pay rise, better pensions, job security and no cuts to redundancy terms.

Details will be announced on 18 November if there are no “substantial” government proposals, the PCS said.