Gordon Matheson, the leader of Glasgow City Council, said the bulk of the organisations' multi-million pound budgets and job creation powers should be handed to local councils.
He argued other functions, such as Scottish Enterprise's role promoting business abroad, should be taken on directly by the Scottish Government.
Writing in today's Herald, he says there is a "compelling case" for abolishing the two bodies, which between them receive more than £500 million funding per year from the taxpayer.
His comments follow Glasgow City Council's call for Scotland's seven cities to join forces to demand more powers from the Scottish Government and spending to be switched from SE and SDS to local government
Cllr Matheson argues: "I believe there's a compelling case to abolish both Scottish Enterprise and Skills Development Scotland. Most of their functions and budgets should revert to local government."
A Scottish Government spokeswoman said: "Just last week the Scottish Parliament endorsed the vital role that our enterprise agencies play in supporting businesses to grow, create employment, increase exports, boost innovation and help Scotland become more globally competitive, a position backed up by the recent Ernst & Young Attractiveness Survey which showed that foreign direct investment projects coming to Scotland in 2012 were at their highest level for 15 years."
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