Senior figures from the EIS teaching union said more than 25,000 people back their call for a pay rise.
Union president Alison Thornton, her predecessor Nicola Fisher and the union’s vice president Bill Ramsay delivered postbags full of signed postcards.
Teaching unions have already rejected a rise of up to 3% from councils - with local authorities describing this as their “best and final offer”.
The EIS insists a 10% rise is needed to start to address a real term decline in teachers’ salaries over recent years and has threatened to ballot for strike action unless demands are met.
Ms Thornton said: “We are delivering over 25,000 signatures to John Swinney today, clearly showing the strength of feeling on the need for a significant pay rise for Scotland’s teachers.
“This represents a very clear challenge to the Cabinet Secretary to demonstrate that he values education and values teachers by ensuring delivery of a fair pay settlement for all teachers this year.
“Whilst it is unfortunate that the Deputy First Minister was unable to accept the cards personally today, we will be taking him up on his offer to meet with us in the near future to discuss the pay campaign.
“The EIS remains committed to seeking a negotiated solution in order to remove any prospect of a formal dispute and would urge the Scottish Government and local authorities to return to the negotiating table with a substantially improved pay offer in the next round of talks.”