Mr Macintosh and party deputy leader Kezia Dugdale have confirmed that they are standing for leadership of the party when Jim Murphy quits next month.
The Eastwood MSP said his supporters were being "bullied and intimidated" into withdrawing their backing.
Scottish Labour said the leadership contest would be conducted "fairly".
A spokesman said Mr Macintosh had since withdrawn his allegations about the party. However, Mr Macintosh insisted his comments still stood but had not been aimed at party staff.
He has not named those he thinks are responsible.
Scottish Labour general secretary Brian Roy said: "I have spoken to Ken Macintosh and he has withdrawn his allegations about the party. The leadership contest in Scotland will be conducted fairly and openly."
In response, Mr Macintosh said: "I am not withdrawing anything. I clarified with Brian [Roy] that the allegations are not against party staff, but against the machine politics which have too much influence in the Labour Party."
Mr Macintosh, the party's social justice spokesman, ran for party leadership against Johann Lamont almost four years ago and is likely to need nominations from six or seven MSPs to be a candidate in this leadership contest.
Ms Dugdale, who is widely regarded as the "obvious person" to take on the job, confirmed her leadership bid on Friday.
But he claims his backers are coming under "incredible pressure to withdraw their support".
"I want to have a contest but I've found the whole weight of the party machine yet again turning against me trying to close down a contest," he told BBC Radio's Good Morning Scotland programme.
"All the people that have been trying to support me, the party machine has turned on them, and they are being put under incredible pressure to withdraw their support. They are being bullied and being intimidated and pressurised not to support me so we don't have a contest.
"I wouldn't even have put my head above the parapet if I didn't know I had that support."
Mr Macintosh, who won a majority of member votes in the last leadership contest, said the three-college system used by the Labour Party to elect leaders was "ridiculous".
"I want the members to take control of the party," he said. "We need to move to one member, one vote."
He called for a quick contest, before the summer if possible, that is "fair and democratic".
By BBC Scotland political correspondent Glenn Campbell
Kezia Dugdale already has the backing of twenty Labour MSPs for her bid to become Scottish party leader. That's more than half the Labour team at Holyrood.
Many of them would like her elected unopposed.
Yet when she announced her intention to stand, Ms Dugdale said she would "absolutely" welcome a contest.
Ken MacIntosh is offering that challenge.
He is likely to require the support of six or seven MSPs to become a candidate. But he claims his supporters are being "bullied and intimidated" by what he calls the "party machine" in an attempt to avoid a contest.
He has not been more specific.
There are certainly those who think a coronation would save time and political energy and allow Labour to concentrate on the 2016 Holyrood election campaign.
Others argue that a contest would allow a fuller debate about Labour's problems and possible solutions and give the new leader more authority to pursue reform.
Mr Macintosh said he would campaign on fairness and social justice across the whole of Scotland with an emphasis on lifelong learning, housing and renewable energy.
"The reason I think it is important that I put my views forward is I think that is all about restoring trust in the Labour Party," he said.
"At the last election people could not bring themselves to put their trust in Labour. I can't believe that after all these years and what we stand for."
Mr Macintosh said restoring the Scottish Labour Party required integrity, principles and honesty and "moving away from machine politics and guile and the idea it's about power and position".
"I'm in politics to make other people's lives better, whether I'm leader or not leader, whether I'm MSP or not MSP. I am a conviction politician," he said.
He said problems with the "party machine" were about "people who want power and position and influence", which was an "issue for all politicians".
"We have to remember our principles and if we can't do that we can't restore confidence in the Labour Party," Mr Macintosh added.
Former East Renfrewshire MP Mr Murphy announced that he would resign next month after Labour's crushing general election defeat at the hands of the SNP.
Ms Dugdale, the Lothian region MSP, said she welcomed a leadership contest.
She has won the backing of more than half of Scottish Labour's MSPs and MP Ian Murray since announcing her intention to stand on Friday.
"I am proud to have already won the support of so many Labour colleagues in the Scottish Parliament," Ms Dugdale said.
"The geographical spread of support I have - with MSPs from north and south, east and west - as well as the backing of MSPs from different parts of our movement shows I can bring our party together."
Scottish Labour MSP Ken Macintosh has told BBC Scotland the "party machine" is bullying his supporters in an attempt to avoid a leadership contest.