The eight core industries had expanded at a rate of 7.2 per cent in the same period last year.
The combined index of these industries - coal, crude oil, natural gas, petroleum refinery products, fertilisers, steel, cement and electricity - was at 159.2 in May, 2013 with a growth rate of 2.3 per cent, according to official data.
"The decline in the growth rate in May was mainly on account of negative growth witnessed in the production of coal, crude oil, natural gas and fertiliser," the Ministry of Commerce and Industry said in a release.
The eight core sector industries have a weight of about 38 per cent in the overall industrial production.
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Petroleum refinery production showed an expansion of 5 per cent. However, the growth was subdued as compared to 23.4 per cent registered in May 2012.
Steel production grew by 4.1 per cent as against 3.8 per cent, while cement output was up by only 3 per cent against 15.4 per cent in the review period.
The growth in eight infrastructure industries was 3.2 per cent in 2012-13 as against 5 per cent in the previous financial year.