Stats NZ data for the three months ended September shows unemployment rose to 3.9 percent in the third quarter, up from 3.6 percent in the June quarter.
The unemployment rate was largely in line with market expectations, and slightly above the Reserve Bank's forecast of 3.8 percent.
The overall Labour Cost Index (LCI) rose 1.1 percent for the quarter.
Wages rose 4.3 percent for the year, with pay in the public sector outpacing growth in the private sector.
Westpac economist Darren Gibbs said the wage increase reflected large settlements in parts of the public sector such as healthcare.
"We do not expect these settlements to continue in the future," Gibbs said.
The under-utilisation rate, a measure of slack in the sector, was 10.4 percent -- representing about 13,000 people. Workers under the age of 24 accounted for most of that growth.
The labour force participation rate was down 0.5 percentage points to 72.0 percent.
"Today's news should leave the RBNZ comfortable with the labour market projections made in the August Monetary Policy Statement, and thus a hike in the (Reserve Bank's official cash rate) at the 29 November meeting remains very unlikely," Gibbs said.
ASB senior economist Mark Smith said labour cost growth appeared to have peaked, though there were risks.
"Wage settlements for care and support workers and in education helped to boost labour costs in the public sector," Smith said.
"The risk is that well-publicised wage settlements could lift wage demands for both public and private sector workers."
Smith expected to see more slack in the labour market slack emerging into 2024.
"Weaker job advertising points to a slower pace of job gains looking ahead, notwithstanding the post-election pick up in surveyed hiring intentions."
Strong growth in the supply of labour looked set to continue, he said.
"As such, we expect the NZ unemployment rate to continue to move up, and to approach 5 percent by the end of 2024, with employment moving below its maximum sustainable level.
"This should further temper wage increases and significantly dampen pressures on core inflation."
