Opposition parties have said the end to the looming threat of council worker strikes would see Scots breathe a sigh of relief but that a deal should have been reached sooner.

Strikes due to go ahead north of the border next week have been suspended after unions received a new pay offer from local authority leaders.

Scottish Labour said people across the country had “suffered weeks of disruption and disarray due to the intransigence of this SNP government” while the Conservatives said the strikes “could and should have been stopped a lot sooner”.

The original deal offered by council umbrella body Cosla was 2% but under the latest offer put out to union members the lowest-paid council workers will see their pay packets go up by around 10%.

Roz Foyer, general secretary of the Scottish Trades Union Congress, said “unions work”.

“This offer could not have been possible without the solidarity of our collective movement. As it should be, it’s now up to the members whether to accept this proposal,” she said.

The deal was reached after marathon talks between First Minister Nicola Sturgeon, Cosla and the unions on Thursday.

Craig Hoy, chairman of the Scottish Conservatives, said the First Minister “was missing in action for weeks”.

“While she was schmoozing around the Edinburgh Fringe with celebrity chums – rather than intervening in a dispute her government was responsible for – litter piled up on the streets outside,” he said.

“This row stemmed from years of systematic underfunding of local authorities by the SNP government, which left Scotland’s councils unable to meet the pay demands of workers grappling with the rising cost of living.”

Mark Griffin, Scottish Labour’s local government spokesman, said the resolution would “come as a relief to millions of Scots and our hard-pressed council workers – but the blame for these weeks of chaos lies squarely with this SNP government”.

“It is simply not good enough that it took weeks of industrial action to embarrass the SNP government into action,” the MSP said.

“This will not be the last industrial dispute of the year. With sector after sector balloting for action, the SNP government must realise that it cannot continue to approach industrial relations in this slapdash and damaging fashion.”

Alex Cole-Hamilton, leader of the Scottish Liberal Democrats, said it was a source of “huge frustration to residents in Edinburgh and across Scotland that Nicola Sturgeon put five festival appearances and a flight to Copenhagen ahead of clean streets and a proper pay deal for workers”.

“The First Minister only turned up to negotiate when it was clear that a deal was about to be done,” he said.

“Now she needs to come to parliament next week and announce a proper funding package that will reverse her decade of cuts to local government.”

Dougie Reid, SNP Cosla group leader, said he was “delighted” a deal had been reached and that “council employees deserve to have their hard work properly valued”.

“The deal brokered and proposed by the SNP focuses particularly on the needs and interests of our lower-paid employees,” he said.

“Given the financial challenges facing budgets in Scotland, I am grateful for the way the Scottish Government and Cosla have stepped up so that the funding and flexibilities needed have been provided.”