MSPs Anas Sarwar and Richard Leonard have emerged as the most likely candidates to succeed Kezia Dugdale.
Ms Dugdale shocked party members in Scotland when she announced on Tuesday night she was stepping down from the job with immediate effect.
She had been leader of Scottish Labour for two years, taking over from Jim Murphy after the disastrous 2015 general election campaign.
Mr Sarwar is the party’s Holyrood health spokesman as well as a former MP and deputy leader of the Scottish party, while Mr Leonard is a former GMB trade union organiser who was elected to the Scottish Parliament in 2016.
Confirming his intention to stand in an article for the Sunday Mail, left-winger Mr Leonard said Scotland needed “a united Labour Party committed to real and bold change”.
He praised the platform put forward by UK leader Jeremy Corbyn and called on the Scottish party to be more “audacious” and take chances to win back support.
Citing issues such as inequality, fuel poverty and public sector cuts, Mr Leonard said: “It is for these reasons that we need a distinctive Scottish Labour vision again - delivered with energy but also with conviction and credibility.
“That is why I decided to seek to be the next leader of the Scottish Labour Party - not simply to be the leader of a strong opposition but to be the next Labour first minister.”
He added: “It is now time to set out our vision of a more equal Scotland with full employment funding quality public services, providing dignity for our OAPs and hope for our young.”
He pledged to continue to “unflinchingly oppose” nationalism, adding: “Labour’s strength is that we organise and represent people across the whole of these islands, as part of a worldwide movement.”
Writing in the same newspaper, Mr Sarwar, who opposed Mr Corbyn in the last UK Labour leadership election, praised him and Ms Dugdale for helping to restore “a confidence in the party that we can win again”.
He insisted that the Scottish leadership contest “will not be about the direction of the UK Labour Party” adding: “We are all united in our desire to elect Jeremy Corbyn as our next prime minister.”
“It will be about electing a leader who can serve our country as the next first minister of Scotland,” he said.
“I firmly believe Labour can achieve power again in both Holyrood and Westminster. We have a radical policy platform that stands in stark contrast to the SNP.
“The next Labour government in Scotland must fix the crisis in our health service.
“We will tackle the crisis in our schools, end the slash-and-burn approach to local government and build an economy rooted in fairness that equips our workforce for the challenges ahead.”
He added: “The next Scottish Labour leader must unite our movement, continue to build confidence among voters and ensure the party are back where we should be - united, radical and in power.”