U.S. architecture billings index up slightly in June

* June billings index up 0.1 point to 45.9

* Project inquiries index up 0.4 points to 54.4

* Third straight month indicating decreased demand

* Weak market conditions persist - AIA

NEW YORK, July 18 (Reuters) - An index of architects' billings that helps forecast U.S. construction activity improved slightly last month, but remained at a level that indicates declining demand for design services.

The architecture billings index rose 0.1 of a point to 45.9 in June, the American Institute of Architects said on Wednesday. The billings index, which measures demand for architects' services, is a leading indicator of construction activity nine to 12 months ahead of the work. Any measure below 50 indicates a decline in billings.

A separate measure of project inquiries rose 0.4 points to 54.4 last month. This measure is usually higher since only some inquiries turn into contracts for design work.

"The downturn in design activity that began in April and accelerated in May has continued into June, likely extending the weak market conditions we've seen in nonresidential building activity," said AIA Chief Economist Kermit Baker.

The monthly billings index is tracked by industrial companies and their investors as an indicator of future demand for machinery and components used to erect buildings. Most diversified manufacturers derive some sales from nonresidential construction of office buildings, retail and warehouse space.

Companies exposed to the sector include Honeywell International Inc, Tyco International Ltd, Ingersoll Rand Plc, Cummins Inc, Eaton Corp , Manitowoc Co Inc, Caterpillar Inc, Deere & Co and Terex Corp.

European companies such as Siemens AG, Schneider Electric SA and lock maker Assa Abloy are also active in the sector.