The American Institute of Architects said the Billings Index for June slid to 51.6, down from 52.9 in May.
When the index tops 50, it indicates growth, while below 50 indicates contraction.
The Institute said, June's score "reflects an increase in demand for design services."
In addition, the trade group's Projects Inquiry Index rose "sharply" in the month, the AIA said, climbing from 59.1 to 62.6.
"With steady demand for design work in all major non-residential building categories, the construction sector seems to be stabilizing," AIA Chief Economist Kermit Baker said in a statement.
"Threats to a sustained recovery include construction costs and labor availability, inability to access financing for real estate projects, and possible adverse effects in the coming months from sequestration and the looming federal debt ceiling debate," Baker said.
The AIA said the Billings index came to 55.6 in the Northeast, 54.8 in the South, 51.2 in the West and 48.3 in the Midwest.