Jack McConnell gave his undertaking at a meeting with the Convention of Scottish Local Authorities on Monday. More details will be revealed when Mr McConnell unveils the Scottish Executive's spending plans next Wednesday.
He acknowledged that the Government's insistence that pay and price increases must be met by "efficiencies" has been "an important discipline but it has also been a tough challenge".
Mr McConnellwill say that the Executive's grant to local authorities is to include "an element" to cover inflationary pay and price rises, initially for three years.
Pat Watters, Cosla's vice-president, said the move "will give us much more leeway in cash terms for pay deals". It has not come in time, however, to bring an end to the dispute involving council staff who are members of Unison.
The union, which has rejected a 2.5 per cent pay offer, also turned down a revised package this week involving a two-stage award of
2 per cent in April and 1 per cent from October.