Job vacancies also rose, while permanent starting salaries saw a sharp increase and hourly pay rates for temps climbed moderately, the latest Bank of Scotland Report on Jobs found.
Recruitment consultancies in Scotland recorded the fastest rise in permanent staff placements for three months, while growth of temp placements was also quicker than in May.
The report found that shortages of available candidates had contributed to pay increases.
It also showed that the Bank of Scotland labour market barometer registered above the 50.0 ‘’no-change’’ mark in June, at 59.7, a three-month high and up very slightly on May’s 59.6 reading.
The barometer measures areas such as levels of staff demand, employment and wages to create a single-figure snapshot of labour market conditions.
June’s figure was broadly in line with its average over 2015 so far, though just below the equivalent index for the UK as a whole.
Growth in permanent and temporary placements was led by Glasgow and Edinburgh respectively, while Aberdeen was the only region where declines were recorded.
Edinburgh recorded the sharpest rise in permanent starting salaries ahead of Glasgow, while Dundee led growth in temp hourly pay rates.
Demand for permanent staff was highest in IT and computing, followed by nursing and medical care, while temporary job vacancies were led by the engineering and construction sectors.
Donald MacRae, chief economist at the bank, said: “Scotland’s labour market continued to perform well in June.
“The number of people appointed to both permanent and temporary jobs rose in the month while the number of vacancies increased.
“Permanent staff pay saw a sharp increase while hourly pay rates for temporary staff rose moderately.
“These results suggest an economy continuing to show moderate growth.”
Business Minister Fergus Ewing said: “We welcome this further evidence that conditions in Scotland’s job market are continuing to improve. The Bank of Scotland report shows that demand for permanent staff is continuing to increase, while permanent starting salaries also grew strongly.
“The report comes at a time when the Office for National Statistics figures published last week show that Scotland’s labour market is performing well across a range of measures. They showed that Scotland currently has the highest employment rate, lowest unemployment rate and lowest inactivity rate of all four UK nations.
“This Government is committed to using every power we currently have at our disposal to build a fair and inclusive jobs market that creates the opportunity for all of Scotland’s people and businesses to fulfil their potential.”