Manpower said the NHS was among the bodies looking to add staff in the public sector, with hiring intentions particularly strong at call centres as ambulance services roll out the new '111' service.
The report said the health service was just one area where an outsourcing of services had led to a readjustment in public sector employment.
Local authorities and central Government are hiring people to manage the commissioning of services, it found.
Mark Cahill, Manpower UK's managing director, said: "We've noticed that a number of public sector organisations have begun recruiting again with renewed vigour.
"Austerity is still the order of the day, but in their efforts to implement budget cuts there has been a degree of over-firing.
"In other words, in their zeal to cut budgets, too many people may have been laid off."
According to Manpower's quarterly look at UK employment, the overall jobs outlook is at its strongest since before the recession, with a slight majority of employers planning to recruit staff.
The study suggested that the jobs market shows no sign of slowing down, although it said thousands of jobs have been created by finance firms to deal with PPI mis-selling.
At least 20,000 jobs have been created to deal with claims over mis-sold payment protection insurance (PPI), Manpower said. These were jobs created by big banks, it said, and did not include those created by companies acting as middlemen for claimants.
Cahill said: "The extra jobs were not a sign of a thriving banking sector, but were linked to the clearing up of mistakes from the past." He expects the jobs boom created by PPI mis-selling to continue.
"Within the last month alone, we have seen big names like Barclays and Lloyds massively raise the amount of money set aside to deal with PPI claims," he continued.
"A whopping £11 billion has already been allocated, and some commentators think that number could easily double. The consequence of this will not only mean cash in people's pockets, it will also translate into jobs."
