The First Minister was responding to a call from interim Labour leader Alex Rowley to use existing powers to reverse a Westminster-imposed cut to Employment Support Allowance (ESA).
The cut to ESA came into force in April for all new claimants placed into the “work-related activity group” – people too ill to work but expected to be able to return to work eventually.
Labour said that if the SNP would not commit to reversing the cut, which takes £30 a week out of people’s pockets, Labour would table amendments to the forthcoming Social Security Bill to do so.
Mr Rowley said: “These are cruel Tory cuts that make a mockery of the claims of Theresa May and Ruth Davidson that the Tories want to build a country that works for everyone.”
The First Minister responded: “This Government will act where we can to mitigate the worst aspects of welfare cuts.
“We know the benefit cuts since 2010 will have reduced welfare spending in Scotland by almost £4bn by the end of the decade.
She continued: “It is important to note that ESA is not one of the benefits devolved to this parliament, and is one of those which will be rolled into the Universal Credit.”
Ms Sturgeon claimed the Scottish Government “could and would do more” if it had powers over the full welfare system.
She added: “I hope, one day, Labour will join us in supporting complete devolution of welfare powers to Scotland.”