Health Secretary Alex Neil said the group - made up of senior Government and NHS officials - will consider how to improve services out of hours, particularly over weekends.
However, nurses' and doctors' leaders have warned additional investment will be required, with health boards already struggling with demand for services.
Several studies in recent years have suggested patients admitted to hospital outwith the standard working week of Monday to Friday, when staffing levels are reduced, have higher death rates.
Earlier this month, Sir Bruce Keogh, the medical director of the NHS in England, unveiled ambitious plans to ensure senior doctors and key diagnostic tests are available seven days a week.
Neil said the NHS already offers "round-the-clock" care, that but more should be done to reduce variations in how it is provided outwith normal working hours.
"We are far from complacent and recognise that care will be delivered differently at 3am in the morning compared to 3pm in the afternoon," he said. "It will be different on a Thursday compared to a Sunday. By focusing additional clinical and non-clinical support at key points over the weekend and overnight, we will be able to improve service provision and patient flow. I am determined to drive forward the changes we need to make this happen."
Neil said moves towards 24/7 care were already happening in some areas, but he wanted to accelerate the pace of change by targeting weekend and out-of-hours services.
He added: "It should mean that pharmacists, physiotherapists, porters - all the services you need to help patients move through and be discharged from hospital - are on hand at the point they are needed to optimise patient care."
In October, Neil announced £4 million of funding for pilot schemes to try out best practices from Europe and North America to improve "patient flow", such as timely discharge of patients, to help hospitals provide round-the-clock care every day of the week.
In England, Keogh has announced hospitals will face sanctions unless they deliver the same standard of care over the weekend.
Ellen Hudson, associate director at the Royal College of Nursing Scotland, welcomed the announcement of the taskforce, but added: "If the priority is to start providing a more comprehensive service seven days a week, the Scottish Government is going to have to provide additional investment to ensure this ambition is actually achievable."
Dr Nikki Thompson, chairwoman of the British Medical Association's Scottish consultants committee, warned spreading "already over-stretched services" more thinly across the week would do nothing to improve the quality or safety of patient care.
She added: "If we are to achieve real improvements in the Scottish health service, it is essential that the Government listens to the views of those staff who are already looking after our sickest patients 24/7, often under huge pressure."