A spokesman for the UKCC (United Kingdom Central Council for Nursing, Midwifery and Health Visiting) said yesterday it was examining Ms Parry's case as a "matter of urgency".
The statement came after it emerged that she started a full-time job this week at the Holy Cross Hospital in Haslemere, Surrey.
Ms Parry, 40, and Lucille McLauchlan, 32, were held in a Saudi Arabian jail for the murder of Yvonne Gilford, a 55-year-old fellow nurse, in December 1996. They were freed by King Fahd of Saudi Arabia in May.
News of Ms Parry's appointment prompted alarm yesterday at the UKCC, which has been considering the case against her for several months.
John Knape, a spokesman, said: "We are investigating the case as a matter of urgency, but at the moment we cannot proceed. Our disciplinary system means that we need one of two things - either evidence of her murder conviction or evidence which backs up the charge. So far we have not been able to secure either from the Saudi authorities."
Although Lucille McLauchlan was found guilty of aiding and abetting in the murder of Yvonne Gilford, the Foreign Office confirmed yesterday that no formal conviction was ever publicly registered against Ms Parry, who faced beheading until her sentence was commuted by King Fahd.
George Galloway, the Labour MP, and two anonymous nurses made complaints against Ms Parry to the UKCC, which has sought legal advice on how it can proceed in the absence of evidence from Saudi Arabia.
Christopher Hinton, the administrator at Holy Cross Hospital, said Ms Parry applied for the post of registered nurse and began working with elderly patients and people undergoing detoxification on Monday.
"She had previously worked at Holy Cross Hospital between June 1982 and March 1983, and had proved herself to be a capable and caring person," he said. "She had many friends among the staff and this friendship helped to sustain her during the difficult months spent in Saudi Arabia. It was consistent with this background that she was considered to resume employment."
The hospital had double-checked her application with the UKCC to ensure she was still registered to practise in Britain. Mr Hinton said her employment was conditional on her registration remaining valid.
Jonathan Ashbee, Ms Parry's brother-in-law, said the nurse had two ambitions at present - "to clear her name and to return to nursing".
He said: "Holy Cross is an excellent place for her to start work again because she knows everyone and has lots of friends there."
But Mr Galloway, MP for Glasgow Kelvin, said that Frank Dobson, the Secretary of State for Health, should "forbid this grisly appointment.
"I wouldn't like any of my relatives treated to her tender loving care and I can't imagine many others would either. At the very least, patients should be warned about the nature of the woman nursing them."