The country received 15.3 mm rainfall from June 7-13 as against 30.6.9 mm, the average rainfall considered as normal for the period, the India Meteorological Department said.
The annual seasonal rains reached Kerala on June 5, four days later than normal, the IMD said.
As per IMD data, 15 out of the 36 sub divisions received deficient rains which include Konkan and Goa, Coastal Karnataka and Kerala, where monsoon had brought its showers.
As many as 13 sub-divisions received scanty rains, while West and East Uttar Pradesh received no rainfall during the past week.
Weather officials said the rains were expected to improve in next week.
Scientists had said that monsoon had begun on a dull note this season with regions along the western coast getting rains and the peninsular region remaining relatively dry.
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Rainfall was excess in Jammu and Kashmir and Andaman and Nicobar islands.
Monsoon rains are crucial for agriculture as only 40 per cent of the cultivable area is under irrigation. The farm sector contributes about only 15 per cent to the country's Gross Domestic Product (GDP), but it employs about 60 per cent of India's population.
On the back of good monsoon in 2010 and 2011, the country harvested a record foodgrains production of 245 million tonnes and 252.56 million tonnes, respectively.