The closely-watched MarkitCIPS construction purchasing managers' index (PMI) hit 49.2 in August, up from 45.9 in July and above economists' expectations of 46.5.
A reading above 50 indicates growth.
Construction activity recorded its fastest fall since June 2009 in July as uncertainty over Britain's decision to ditch the European Union triggered a steep fall in commercial building activity.
However, business activity only recorded a marginal fall in August, as new order volumes "moved closer to stabilisation."
The report said the rate of contraction in housing activity and commercial building was the slowest for three months, while civil engineering was stable after falling in July.
The update follows a surprise swing in manufacturing output in August, notching up its highest monthly rise in a quarter of a century.
Tim Moore, senior economist at Markit, said the report only highlights "a partial move towards stabilisation" and not a return to "business as usual" for the construction sector.
"The downturn in UK construction activity has eased considerably since July, primarily helped by a much slower decline in commercial building.
"Construction firms cited a nascent recovery in client confidence since the EU referendum result and a relatively steady flow of invitations to tender in August."
He said there were still widespread reports that Brexit uncertainty was dampening demand, with total new order volumes continuing to fall in August.
"Despite another month of reduced output, the latest figures can be viewed as welcome news overall after a challenging summer for the construction sector," he added.
"The move towards stabilisation chimes with the more upbeat UK manufacturing PMI data for August, and provides hope that the near-term fallout from Brexit uncertainty will prove less severe than feared."
The returning strength to the construction industry filtered through to employment, with staffing levels recording a small expansion in August. The report said the use of sub-contractors had continued to decline.
However, sterling's plunge to 31-year lows since the Brexit vote had ramped up costs for construction firms, as input cost inflation grew for the third month in a row and hit its highest level for five years.
The construction industry's better-than-expected PMI comes after official figures published last month showed the industry had fallen back into recession for the first time in four years.
The Office for National Statistics (ONS) said construction output dropped by 0.7% in the second quarter, following a 0.3% fall in the first quarter, meaning the industry recorded two consecutive quarters of negative growth for the first time since 2012.
Howard Archer, chief European and UK economist at IHS Global Insight, said August's PMI still points towards a struggling construction sector.
"There is certainly not the bounce back in construction activity in August that was seen in the manufacturing sector according to the purchasing managers.
"Nevertheless, the near-stabilisation in construction activity in August reported by the purchasing managers following on from manufacturing activity bouncing back to a 10-month high adds to the mounting evidence that the economy has so far held up pretty well following June's Brexit vote."
He said that while the economy is holding up well, there is concern that it will lose momentum in the coming months as uncertainty rises over when Article 50 will be triggered.
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