Fears are growing over the future of the hospital in Glasgow as health boards in different parts of the country debate whether they should continue to send patients there.
Supporters of the hospital - also known as the centre for integrative care - were among the audience at NHS Greater Glasgow and Clyde's (NHS GGC) annual review, where Mr Neil and members of the public questioned health board staff.
Catherine Hughes, who has used the homeopathic service, told the audience of 200 it was wrong for the staff and patients to again be facing uncertainty about the future of the hospital.
Robert Calderwood, chief executive of NHS GGC, said that while the board had no plans to close the centre more than £700,000 of funding came through referrals from other boards. If this money vanished, he said, it would spark a discussion with staff over the future running of the hospital.
However, Mr Neil said: "I am absolutely determined not only that we keep the centre for integrative care open, but that we also continue to develop its services because I believe it has a significant contribution to make to healthcare not only in Glasgow but across Scotland.
"Anyone who is worried about the centre closing, there is no prospect of us allowing that centre to close."
Homeopathy is a controversial system of medicine which involves treating patients with highly diluted substances, given mainly in tablet form, with the aim of triggering the body's own healing mechanisms. Some doctors say there is no evidence it works and it was dismissed at one British Medical Association conference as witchcraft.
NHS Highland became the first Scottish health board to stop new patients being referred to homeopathic services in 2010 and NHS Lothian followed suit earlier this year, although it is facing a legal challenge. NHS Lanarkshire is also looking into the issue.
However, supporters emphasise that it offers a wide range of other treatments including traditional medicine.
Following the annual review, which took place in central Glasgow yesterday, Mr Neil said he saw the hospital expanding its role.
He said: "I think, for example, we are looking at how we can enhance right our chronic pain services and there is no doubt in my mind at all the centre for integrative care could have a significant role in helping us to implement a chronic pain strategy not just in terms of servicing Glasgow but in servicing Scotland."
Mr Calderwood said he would like to see the centre continue and at the moment some Scottish patients had to travel to Bath to receive treatment for chronic pain.
However, he said if there came a point where funding from other health boards had trickled away and further savings could not be found there would have to be a discussion with the board. NHS GGC provides £1.5 million of the total £2.2m funding pot.
Ms Hughes described Mr Neil's comments as "really positive" but said that patients remained concerned.