Fitch said prospects of a swift economic turnaround have been further dented by a 20 % fall in the domestic currency since the end of May due to increased concerns over the country's large current account deficit.
The sharp cut in the growth forecast comes when the country faces challenges such as slowing growth, exchange-rate woes and concerns about the current account deficit.
India's economy expanded at a 4.4 % pace in the April-June quarter compared with 4.8% in January-March.
"Demand is weak, both externally and domestically, which is a large drag on the economy," the agency said Fitch also cut India's growth rate projection for FY'15 to 5.8 % from the June forecast of 6.5 %.
In September 2012, the company had projected a growth of 7.5 % for FY'15.
Last week, the Prime Minister's economic advisory council had revised its growth forecast for the current financial year to 5.3 % from 6.4 % projected earlier.