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Members of two of Scotland's biggest teaching unions have overwhelmingly rejected a "final" pay offer.

The Educational Institute of Scotland (EIS) and Scottish Secondary Teachers Association (SSTA) warned of industrial action if the offer was not improved.

The government and councils had offered a headline 3% rise, with bigger increases for staff on lower grades.

Council body Cosla said the unions' demand for a 10% increase could not be met in a single year.

Education Secretary John Swinney said he was disappointed by the rejection of a "strong and fair" offer.

The teaching unions claim the real value of teachers' pay has fallen by 20% over the past decade, and a big rise is needed to boost recruitment and retention of staff.

Last month tens of thousands of teachers marched in Glasgow in support of a "fair deal" that would "value teachers".

The education secretary has said the current offer would give the majority of staff a rise of between 5% and 11% once restructuring and pay progression were factored in.

The EIS said 98% of members who voted rejected the offer, with a turnout of 74%. In the SSTA ballot, 97% rejected the deal, on a 73% turnout.

EIS General Secretary Larry Flanagan said: "Today's near unanimous rejection of the pay offer is a landmark result, one of the strongest rejections of an offer in EIS history, and one which is indicative of the current mood of Scotland's teachers, increasingly agitated on pay but angry also at excessive workload, mainstreaming on the cheap, and austerity driven cuts to resources."

SSTA general secretary Seamus Searson said the vote sent a "strong message" to the Scottish government.

He said: "It is time for government to return to the negotiating table and treat teachers with respect and seek a meaningful settlement."

A third teaching union, the NASUWT, said survey of more than 1,000 of its members suggested more than half were willing to take industrial action in support of the claim.

The unions said they hoped to make progress through negotiation, but the EIS warned it could ballot for industrial action in the New Year if an improved offer was not made by Christmas.

Gail Macgregor, resources spokeswoman for Cosla said: "The trade unions claim for 10% increase in one year cannot be met within the resources we currently have available."

Mr Swinney, who is also the deputy first minister, said: "This was the best pay deal in the UK for 2018-19 so it is disappointing that teachers have rejected what I believe was a strong and fair offer.

"All teachers on the main grade scale were offered at least a 5% annual increase, with some receiving up to 11% in conjunction with their annual progression.

"I am pleased there will be further talks and we will engage positively with the unions and with Cosla to seek to strike a pay deal."