The reserves had declined by $1.74 billion and $1.80 billion respectively in the previous two weeks of June 1, 2012.
The RBI was believed to have sold dollars during these weeks to curb the slide in the rupee's value.
The partially convertible rupee slumped to a record low of 56.52 against the US dollar on May 31.
It has weakened sharply in the last two months due to increased demands from oil importers and outflow of money by the foreign institutional investors (FIIs), as poor GDP (gross domestic product) growth data dampened sentiment in the Indian markets.
Foreign currency assets, the biggest component of the forex reserves kitty, grew $1.49 billion to $254.59 billion during the week ended June 8, according to the RBI's weekly statistical supplement.
The RBI did not provide any reasons for the change in foreign currency assets.
It said that the assets expressed in US dollar terms included the effect of appreciation or depreciation of non-US currencies such as the pound sterling, euro and yen held in reserve.
The value of gold reserves remained the same during the week under review. The value had declined in the week ended June 1, 2012 by $1.03 billion to $25.58 billion.
The value of special drawing rights (SDRs) grew by $13.3 million to $4.35 billion, and India's reserves with the International Monetary Fund (IMF) increased by $8.7 million to $2.84 billion.