The report also found that temporary jobs increased at a sharper rate, with the pace of expansion the highest since March 2011.
The report found that permanent staff salaries continued to rise in November. Although moderate, the rate of inflation was the sharpest for 14 months. Temporary pay also increased, but the rise was only marginal.
Demand rose for seven categories of permanent staff during November. The only exception was the hotel and catering sector, where a marginal reduction was signalled. The strongest expansion was indicated for engineering and construction workers. Other sectors that saw a rise in permanent staff placements were IT and computing, and secretarial and clerical jobs.
REC chief executive Kevin Green said: "Recruiters are reporting another monthly increase in the number of people they have placed into permanent and temporary jobs and it's beginning to look like an accelerating trend.
"Employer confidence is genuinely bouncing back with businesses feeling more encouraged to hire, which bodes well for the New Year.
"The reductions in corporation tax and investment in big infrastructure projects announced in the Autumn Statement should help boost confidence even higher and encourage more job creation in 2013."
Bernard Brown, partner and head of Business Services at KPMG, said: "Twelve months ago employment prospects were bleak. Today, however, the negative outlook has been replaced by cautious optimism as employers gradually gain confidence to make decisions about the vacancies they want to fill.
"Perhaps the Government's long-term strategy for jobs is beginning to bear fruit.
"With the latest figures hinting that robust demand in business is offsetting weak demand across the public sector, we might just be seeing signs of resilience."
Brown added: "But before anyone gets the bunting out, the good news must be seen in the context of a fragile economy that remains susceptible to future shocks.
"Recovery is by no means certain and we need a few more months like this to suggest that emerging trends are translating into a sustained period of growth in employment."