However, the growth in the month under review has shown a marginal improvement over the previous month, when the sectors registered a growth rate of 1.6 per cent.
The key infrastructure sectors had recorded growth of 4.9 per cent in December 2011.
The cumulative expansion of these industries in April-December 2012 slowed to 3.3 per cent from 4.8 per cent in the same period previous year, according to the official data released today.
The eight industries include crude oil, petroleum refinery products, coal, electricity, cement and finished steel and have a weight of 37.9 per cent in the overall Index of Industrial Production (IIP).
The decline in growth in December 2012 was "on account of negative growth witnessed in the production of coal, natural gas and fertiliser", it said.
Economists said that the under performance of the core sectors points towards economic slowdown. These numbers will have implications on industrial production data for December to be released later next month.
"These sectors are continuously under performing. It will have its effect on IIP as well," Crisil chief economist D K Joshi said.
Belying expectations of recovery, economic growth slipped further in the July-September quarter to 5.3 per cent, raising fears that the slowdown may pull down the annual growth rate to decade's low level.
Production of natural gas and coal contracted by 14.9 per cent and 0.2 per cent, respectively, in the month under review. Fertiliser output too shrunk by 3.8 per cent against 0.8 per cent growth in December 2011.
Steel and electricity production slowed to 5.2 per cent and 4.4 per cent, respectively, in the reported period against 10.2 per cent and 8.9 per cent, respectively, in the year-ago period.
Cement output slowed to 3.9 per cent from 13.6 per cent in December 2011.
However, crude oil and petroleum refinery output grew by 1 per cent and 5 per cent against the fall of 5.5 per cent and 0.7 per cent, respectively, in December 2011.
The growth of eight core sector industries had declined to 1.8 per cent in November 2012.