Mr McLeish has been pressed for answers over the affair
Henry McLeish has attempted to play down the controversy over his office expenses, calling the affair "a muddle not a fiddle".
He said he regretted the matter, but he insisted he would continue as first minister.
Mr McLeish, in an interview with BBC Scotland, explained that his constituency office in Glenrothes, Fife, had generated £36,000.
He said the money had been raised through five sublets since he first became an MP in 1987, with the aim of improving the service he offered to his constituents.
The first minister stressed there was no personal gain from the money raised.
Mr McLeish has already paid back £9,000 to the House of Commons Fees Office, but he said he is prepared to pay back the full amount from his own pocket if required.
Mr McLeish said: "There were five tenants who paid an income of just over £36,000 over the 14 years.
"That money was used entirely for my office account and that meant for the benefit of the constituents in Central Fife.
"What I think is important to stress is that the income from the fees office and the income from the sub lets was only used for one purpose - my constituents.
'Mistake'
"There was no personal gain involved, there was no political gain."
He said the cash had been spent on "general run-of-the-mill office items" rather than staffing.
"I was determined to provide the absolute best service I could and the important point is that I should have declared it at that point.
"I regret very much that mistake."
Mr McLeish is due to face his critics in the Scottish Parliament in a debate about the matter on Thursday.
His decision to speak to the media ahead of that debate has been seen as an attempt to draw a line under the affair.
He said: "This should have been done quicker, this should have been done better than it has.
"What I am looking to do is get into the public arena all the information, all the letters I have exchanged with Westminster.
"I have simply nothing to hide - no personal gain, no political gain."
The first minister said it had not occurred to him to declare the income.
Mr McLeish explained that the Fees Office had come up with the figure of £9,000 which he has already repaid in relation to law firm Digby Brown, which rented an office from him for just over two years.
'No resignation'
"My main issue all along was to allow the parliamentary authorities to deal with this and then agree to anything they say," he said.
"That was the position, the £9,000. It remains the position with the new information I am providing to them."
He said he was willing to repay the full amount if asked to do so by the Fees Office - and that he would pay it out of his own pocket.
"It is important to say that it would not come from Westminster allowances, because those have ceased.
"It would not come from the new parliament in Edinburgh because that would be totally inappropriate.
"What would be important would be if the Fees Office said that was required or some figure was required I would honour that."
Turning to other allegations over the use of his office, he said: "It has never been used as a campaign headquarters. It wasn't about political purposes, it was a correspondence address."
The opposition has demanded Mr McLeish's resignation over the row, but he has insisted he will not be standing down.
Mr McLeish said: "I look forward to continuing as first minister.
Fully comprehensive account
"It has been a very good 12 months, a lot of things are happening in Scotland, there is a new confidence."
Earlier Mr McLeish had given Labour colleagues a "fully comprehensive account" of the affair.
And Mr McLeish's colleagues spoke in support of the First Minister as they left the Parliamentary Labour Party meeting.
Health minister Susan Deacon described the meeting as "very positive", while finance minister Angus MacKay said he was "very happy" with what he had heard.
These sentiments were echoed by the Parliament minister, Tom McCabe.
Senior backbenchers also spoke of their confidence in the First Minister.
East Kilbride MSP Andy Kerr said Mr McLeish had received a round of applause from his colleagues who had given him their "full support" during the meeting.