Deputy First Minister John Swinney yesterday ruled himself out of the race to be the next leader of the SNP.
Mr Swinney said he had to do what was "right for my family, the Scottish National Party and our country".
It comes after the SNP's national executive said the new leader will be confirmed on Monday, March 27.
Nicola Sturgeon announced on Wednesday that she was resigning after eight years as SNP leader and first minister.
Mr Swinney, who has been a member of the Scottish Parliament since 1999, served as leader of the party between 2000 and 2004.
He had been tipped for a return to the top job and admitted he had "thought carefully about whether I should stand".
Fresh perspective
But, in a post on Twitter, Mr Swinney said he had instead decided to "create the space for a fresh perspective to emerge".
He added: "For the best part of the last 40 years, I have had the privilege of being at the very heart of formulating the strategy of the SNP.
"From a very poor starting point in the 1980s, I am proud to have played my part in building the SNP into a successful party of government in Scotland with an impressive electoral record."
Nominations for the post of SNP leader have already opened and will close at noon on Friday, February 24.
The party's national executive said the new leader would be selected on a one-member-one-vote basis.
Who will succeed Sturgeon?
The BBC says possible contenders include:
- Kate Forbes, finance secretary. Currently on maternity leave.
- Angus Robertson, who previously headed the SNP's Westminster group.
- Humza Yousaf, health secretary, who has held several senior posts in government.
- Keith Brown, justice secretary.
Two other high-profile SNP figures previously tipped to replace Ms Sturgeon have also ruled themselves out.
The party's leader at Westminster, Stephen Flynn, said the top job should go to an MSP.
And, confirming she would not stand, fellow MP Joanna Cherry said the SNP "needs a leadership election that is about policies and not personalities".
Ms Sturgeon plans to remain in office until her successor is elected.
Criticism of the SNP leader on a number of issues had been steadily mounting in recent months, but few people could have forecast this weerk's developments.
Ms Sturgeon made her resignation announcement at a hastily-convened news conference at her official Edinburgh residence, Bute House, and insisted it was a decision she had been weighing up for some time.
"In my head and in my heart I know that time is now. That it's right for me, for my party and my country," she said.