At Holyrood, Mr Mackay said the government would take inflation into account in future pay policy, adding that the “time is up” for the cap.
Mr Mackay said: “The Scottish government will take into account inflation in the future pay policy.
“Remember that what the Labour party proposed was basic-rate tax rises for the workers of Scotland, including public sector workers.
“We will take a reasonable approach that absolutely recognises that the time is up for the one per cent pay cap. Not only will the SNP commit to that, but we will do it.”
Mr Mackay’s comments came after the Tories and the DUP combined at Westminster to reject a bid by Labour to scrap the limit.
The defeated Labour amendment to the Queen’s Speech was supported by SNP MPs.
The vote followed signals that the UK government was considering abandoning the cap. These were later denied by Downing Street.
The approach taken by the SNP at Westminster led to Labour calling on the Scottish Government to lift the cap in Scotland.
Mr Mackay’s comments were welcomed by Scottish Labour leader Kezia Dugdale.
She said: “It is high time that our public sector workers get the pay rise they deserve. This U-turn has only come about because Labour shamed the SNP into backing our policy.”