Consistent selling of dollars by some foreign banks and unwinding of short-term forward contracts by exporters mainly boosted the sentiment for the local unit, dealers said.
The overall forex market sentiment was largely perturbed by the global central bankers' meet at Jackson Hole which begins today, they added. Traders are awaiting for US Fed chair Jenet Yellen's speech tomorrow for hints over the US central bank's policy stance.
Meanwhile foreign portfolio investors continued to remain net sellers in equity markets as they sold shares worth Rs 696 crore on net basis today, provisional exchange data showed.
The home currency resumed on strong note at 64.03 from last close of 64.12 at the Interbank Foreign Exchange market.
It later hit a fresh intra-day high of 64.02 in late afternoon deals before ending at 64.04, showing a smart rise of 8 paise, or 0.12 per cent. This is the best closing for the rupee since August 9, when it had settled at 63.84.
For the week, the Indian unit has appreciated by 11 paise after two-straight week fall.
Forex market will remain closed tomorrow for Ganesh Chaturthi.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0676 and for the euro at 75.5805.
In cross-currency trades, the rupee strengthened further against the pound sterling to close at 82.07 from 82.17 per pound and rebounded against the Euro to settle at 75.54 from 75.66 earlier.
It also bounced back against the Japanese yen to end at 58.53 per 100 yens from 58.72 yesterday.
The benchmark six-month premium payable in January edged down to 120.50-122.50 paise from 122-124 paise, while far forward July 2018 contract also moved down to 257-259 paise from 258-260 paise.
On commodity front, benchmark Brent crude was down 5 cents a barrel at USD 52.52 in early Asian trade, U.S. Light, sweet crude was 10 cents lower at USD 48.31 a barrel.
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