The PMI, which indicates business growth with numbers above 50, rose from 52.3 to 53.2, said the report, which is co-produced by Markit Economics.
For the first time in nine months, all three component indexes -- housing, commercial engineering and commercial construction -- rose in the month. The overall index, however, remains below its historic average.
"Confidence over future business prospects remained relatively muted," the report said.
"The survey suggests that the sector should make a positive contribution to the economy in the final quarter of the year," Markit economist Sarah Bingham said.