The new estimate compares with projections of 5.7 per cent made in June and 7 per cent in September, underlining the "severity of the growth shock," the rating agency said in its 'Global Economic Outlook' report released on Thursday.
Fitch said prospects of a swift economic turnaround have been further dented by a 20 per cent 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 per cent pace in the April-June quarter compared with 4.8 per cent 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 per cent from the June forecast of 6.5 per cent. In September 2012, the company had projected a growth of 7.5 per cent 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 per cent from 6.4 per cent projected earlier.