Colleges currently have waiting lists amounting to 21,280 applications – more than double original estimates from a survey by The Herald last month.
There is now mounting pressure on Education Secretary Michael Russell to increase the number of student places through additional funding.
The amount of money colleges get for teaching has been cut by nearly 16% between 2010/11 and 2012/13 – from £460 million to £387m.
The cut comes at a time when around one-quarter of 16 to 24-year-olds in Scotland are out of work.
The new waiting-list figure does not represent the number of individual students involved because it is common to make more than one application.
There may also be cases where students have found a place at another college or gone back to school, but remain on a waiting list.
However, the new figure was seized upon by colleges, lecturing unions and student leaders as evidence of unmet demand.
John Henderson, chief executive of Scotland's Colleges, said: "Demand for college places is high, this demand is not always being met and colleges are having to turn people away.
"While it is possible some individuals will be on waiting lists for more than one course, that in itself cannot account for the high number.
"Colleges are facing significant ongoing cuts to core teaching budgets and, while they will always strive to be more efficient, the ability to meet demand and maintain quality and breadth of provision will be increasingly difficult."
Larry Flanagan, general secretary of the Educational Institute of Scotland, which represents lecturers, blamed cuts.
"These cuts have cost many lecturers and support staff their jobs and led to a narrowing of course provision," he said. "The end result is many thousands of young people have seen their opportunities for further education greatly diminished."
Robin Parker, president of NUS Scotland, called for college places to be expanded.
"Given the current lack of employment opportunities, there is a real risk of these people moving from waiting lists to dole queues," he said.
However, Mr Russell said it was "absolutely wrong" to suggest 21,000 people were on waiting lists who had been denied a place in learning.
"No previous government has ever matched our guarantee ... that every 16 to 19 year-old in Scotland not in education, training or a job is guaranteed an offer of a place in education or training," he said.
"Colleges exist to give people the skills needed to get a job and also respond to employer need, therefore, offering courses which are economically relevant.
"Furthermore, some colleges are continuing to advertise course vacancies, meaning that waiting lists for some opportunities are not the way to accurately measure overall demand."
The row over the waiting-list figures follows a survey by Scotland's Colleges of the country's 43 colleges, of which 36 responded. Subject areas with the highest waiting lists included health care, health and safety, personal care and appearance and engineering.
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