The services sector added employees at the fastest rate on record, matching the 55.4 reading hit in September 2013. Last month it read 52.8.
Markit's "flash" composite PMI, a weighted average of its manufacturing and services indexes, hit 61.1 in June, also a record high, versus 58.4 in May.
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"Importantly, this is not just a rebound from the weather-related disruptions to business seen earlier in the year," said Chris Williamson, chief economist at Markit. "Companies are reporting strong demand for goods and services, linked to growing confidence among households and business customers, setting the scene for further robust economic growth as we move into the second half of the year."
He said growth in excess of 3.0 percent for the second quarter "would not be a surprise."