Announcing his candidacy for the SNP leadership on Thursday, Mr Swinney dismissed the push for the country to go to the polls as a “red herring”.
But Scottish Labour deputy leader Dame Jackie Baillie said there should be a Holyrood poll as well as the upcoming UK general election “to boot both of Scotland’s failing governments out for good”.
She added: “Scotland’s public services are in chaos and the ruling SNP is in disarray – but all they are offering Scots is yesterday’s man and serial failure John Swinney.
“When the Tories began their revolving door policy in Downing Street the SNP rightly demanded an election, but now they are saying Scots should put up and shut up with a revolving door in Bute House.
The SNP is denying democracy
Dame Jackie Baillie
“No Scot voted for first minister John Swinney or the latest collection of SNP politicians that will make up the next cabinet.
“The SNP is denying democracy – that position is untenable.
“It’s clear for all to see that they are running scared of the verdict of the Scottish people.”
Mr Swinney looks set to become first minister next week following a tumultuous period in Scottish politics.
Current incumbent Humza Yousaf announced last Monday he would step down rather than face a no confidence vote in Holyrood which he may have lost.
Mr Swinney and former finance secretary Kate Forbes – who Mr Yousaf defeated in last year’s leadership contest – quickly emerged as the front-runners to replace him.
But Ms Forbes ruled herself out on Thursday and instead looks set to take up a key place in Mr Swinney’s government, should he win the leadership and subsequently be elected first minister.
Nominations for the SNP’s top job close on Monday at noon, with Mr Swinney to be declared the winner if no other candidate gains the 100 signatures from 20 different branches required to run.
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A spokesman for the SNP said: “Calls from Jackie Baillie for a Holyrood election are completely hypocritical. Just last month the Labour Party appointed a new First Minister in Wales with no election held.
“There is a difference between Westminster and Holyrood electoral systems. We have a fixed-term parliamentary system at Holyrood.
“In Westminster, MPs don’t elect who the Prime Minister is; however at Holyrood, MSPs do elect the first minister.
“There will be a vote in the Scottish Parliament, depending on who the SNP elect as it’s new leader.”