Local government body Cosla made the two-year offer for approximately 250,000 local authority workers after union members voted against strike action and to accept a one-year deal, hoping to negotiate upwards after that.
The offer to staff, coming on the back of a pay freeze, has however not yet been accepted by all the unions involved.
But local authority leaders are hoping the promise of a further 1% rise in 2014-15, as well as their commitment to match the new level for the living wage when it is announced in November, will help secure the deal.
Councillor Bill Hendry, Cosla's human resources spokesman, said: "I am delighted to announce to the local government workforce that Cosla leaders have today provided them with certainty over pay for this year, and perhaps more crucially, for next year.
"They have done this by extending a pay offer of 1% for this year by a further 1% from April 1, 2014 for the year 2014-15.
"This extended offer will also include a commitment to match the living wage level to be announced in November this year by the Living Wage Foundation."
He added: "In very difficult financial circumstances, council leaders have given the whole workforce a 1% pay increase for each of the next two years, and in addition to this they have given a commitment to increase the hourly rate to match that recommended by the Living Wage Foundation from April 1 2014.
"This commitment will be most welcomed by the trade unions as it puts additional money into the pockets of those members of our workforce who are the lowest paid."
But the largest local government union, Unison, did not agree with the offer, saying it undermined the previous acceptance of the one-year deal.
The union will meet next week to discuss the offer and the industrial action its members recently rejected.
Dougie Black, Unison's lead negotiator in local government, said: "We consulted in good faith on the employers' final offer which was a one-year deal. Our members decided not to take industrial action in support of an improved offer and therefore we accepted the offer and wrote to the employers to accept.
"It is disingenuous of the employers to then undermine that position by making a further offer that has been made outside the accepted bargaining machinery, as was the first offer.
"There comes a point where we wonder about the credibility of the bargaining machinery if this is the way the employers treat it."
Alex McLuckie, of the GMB union, said they would consult with members on the offer.
However, he added the pay rises proposed were below the rate of inflation.
Mr McLuckie, GMB Scotland's senior organiser for public services, said: "We have just received notification of this latest offer.
"GMB will need to consult with our members to determine if this is acceptable.
"However, GMB welcomes the increase in the living wage. GMB Scotland fought long and hard to establish a living wage in local government and it is good to see it being continued into 2014/15.
"Our concern on this and previous offers is the general increase.
"This is the fourth year that pay increases have lagged well behind the rate of inflation, resulting in a significant drop in the living standards of local government workers in Scotland.
"We would like to see this addressed in any pay offer."