The Scottish Police Federation (SPF) and the Association of Scottish Police Superintendents (ASPS) are now supporting the reform of the legislation in a move which was seen as a marked shift in position by members of Holyrood's Justice Committee.
The two policing organisations denied they had drastically changed their positions but faced accusations of backtracking on their previous stance.
Tony Kelly, of law reform group Justice Scotland, said: "I am surprised because the Police Federation concerns have always been reasonable. We need to have new safeguards and a wider review if we are to abolish corroboration."
Senior members of the judiciary have previously joined the Faculty of Advocates in expressing concern that removing the need for evidence to come from two sources could cut conviction rates and lead to miscarriages of justice.
Richard Keen, QC, dean of the Faculty of Advocates, said: "It is a surprising U-turn given the increasing weight of evidence in support of the need for a detailed analysis of the implications of abolition of corroboration. The view of the faculty has been consistent from the outset. We consider that this matter should be the subject of review by the Scottish Law Commission."
The change to the legal principle for evidence to be double-sourced is part of the Criminal Justice Bill being considered by MSPs. The Scottish Police Federation has until now been wary of abolishing corroboration due to fears that removal could "open the way to spurious and malicious allegations".
The Association of Scottish Police Superintendents, which represents more senior ranks, was previously "not wholly convinced" by the case for scrapping corroboration. But both now support the reform, it emerged, as representatives of the two bodies gave evidence to the Justice Committee.
Independent MSP John Finnie, an ex-police officer and ex-SPF official, quoted from written evidence submitted by the federation which stated that "corroboration is particularly important in maintaining public confidence in the criminal justice system".
He asked: "What has changed?"
SPF vice-chairman David Ross told the committee: "I don't consider that we have turned our position completely from one of resistance to one of support.
"I think, as our understanding has grown about what we are talking about here, our position has moderated to the extent we would support the removal of the requirement of corroboration, in general terms, in favour of the requirement for a sufficiency of evidence, across the whole of the evidence, to prove guilt beyond reasonable doubt."
David O'Connor, president of ASPS, had said in written evidence he remained "not wholly convinced of the case for the complete abolition of the requirement for corroboration".
Mr Finnie asked: "I would take that as unconvinced. What is the position of ASPS? Are you for it, or against it?"
Mr O'Connor said: "We are more content with the proposals in moving forward, provided that as we move forward we are quite clear on what the marking rules will be. We have heard a great deal about not just looking at the quantity of evidence but the quality."
Mr Finnie said the staff associations' positions had clearly "evolved".
Mr O'Connor replied: "At the outset of the debate we had concerns about the wholesale abolition of corroboration, and there has been some clarity brought to the debate. We had concerns we would potentially end up with a case where you would have a move away from the criminal burden of proof to something more like the civil burden of proof.
"One of the key safeguards for us is that we're retaining the criminal burden of proof, that we have to prove a case beyond all reasonable doubt."
But committee convener Christine Grahame said: "That was always the case."