The headline purchasing managers index for the construction sector hit 58.9 in September, just a whisker below the six-year high of 59.1 in August, the research firm said.
However, September marked the fifth consecutive month the index has registered above the break-even level of 50.
Of the three sub-sectors, residential housing construction was the strongest performing, Markit said, with activity at the highest point in nearly a decade.
Commercial construction grew at the fastest pace since May 2012. Civil engineering, meanwhile, slipped slightly in the month.
Markit said new project orders rose in the month, helping to push a gain in employment numbers for the fourth consecutive month.
The rate of job creation in construction reached the fastest pace in September in just under six years, Markit said.
Beyonce flaunts bikini body, Blue Ivy in vacation pics
Couple mistakenly served bag of cash at McDonald's drive-thru