Mr Neil has been accused of misleading Parliament and breaking strict rules on ministers' conduct after emails showed he instructed NHS Lanarkshire to change its plan to concentrate acute mental health services at Wishaw and Hairmyres hospitals.
Instead, he told the health board to retain beds at Monklands hospital, in his Airdrie and Shotts constituency, despite warnings that the move would result in a "less than optimal service" for patients.
Later the same day he handed responsibility for the shake-up to his deputy, Michael Matheson, to avoid a conflict of interest which could have placed him in breach of the ministerial code of conduct.
He subsequently told MSPs he was not involved.
Labour yesterday highlighted an email from the head of NHS Lanarkshire, shortly after Mr Neil issued his instruction to keep beds at Monklands, warning there was "no alternative option" to the original plan which could "deliver the same benefits" for patients.
Ian Ross also told the head of the NHS, Derek Feeley, that "service-users and carers are fully supportive of the proposed developments".
Another email, also obtained under Freedom of Information, suggests that Mr Neil pressured his predecessor as Health Secretary, Nicola Sturgeon, to delay a decision on the shake-up until after local elections.
The case dates back to 2012, when Mr Neil became Health Secretary.
He stepped in to reverse the original plans within days of taking over in the job. Earlier this week, Alex Salmond dismissed Labour calls to sack him.
Labour's health spokesman Neil Findlay yesterday wrote to Ms Sturgeon asking whether she agreed with Mr Neil's actions.
He said: "The explanation offered by Alex Neil and his boss Alex Salmond was completely unsatisfactory and these new revelations put more pressure on the Health Secretary.
"It was clear from the medical advice that these proposals were in the interests of patients but because it did not suit him politically he forced NHS bosses to put back a decision until after the local authority elections.
"The fact that the chief executive of NHS Lanarkshire was still 100% behind the changes and cited the support from 'service-users and carers' as one of the key reasons right up until Alex Neil overruled him shows what a mess Alex Neil has made of this."
Mr Findlay added: "Alex Neil has put his own political interests before patients and then deceived the Scottish Parliament to cover it up.
"He is not fit for office and should be sacked if he does not have the decency to resign."
A Scottish Government spokesman said: "As we have consistently made clear, on his appointment as Health Secretary, Mr Neil wished to review a number of key decisions, including the proposals about to be put forward by the board of NHS Lanarkshire on mental health services.
"With over 500,000 people resident in NHS Lanarkshire's area, Mr Neil addressed his concerns on the service change to the region as a whole.
"He was clear in his view that acute mental health facilities would be best retained at Wishaw General Hospital, Monklands Hospital, and with a unit at Hairmyres Hospital."
A spokesman for Mr Neil said: "Clearly frustrated at failing to get anyone to take their damp squib demands seriously, Labour have resorted to more pathetic recycling of well-known facts."