The Scottish Government wants free nursery provision for three- to four-year-olds increased from 475 hours to 570 hours a year by August 2010.
But Edinburgh estimates this will cost an extra £800,000 a year, and has asked the Scottish Government for more money to help it cope.
A council spokesman said: "We are committed to meeting this target but if there is not extra money we will have to look elsewhere across our services to see where savings can be made."
Edinburgh is the first council to admit to such difficulties in meeting the target. Other councils in Scotland are set to calculate the estimated extra cost later this year. A spokesman for Aberdeen City Council said it would be looking at the issue in the autumn.
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