The local currency was also boosted by consistent capital inflows and dollar sales by exporters.
The Reserve Bank of India on Tuesday allowed swap facility for term deposits of lenders and relaxed norms for banks to borrow funds from overseas.
US President Barack Obama said he would pursue diplomatic efforts to remove Syria's chemical weapons, giving rise to hopes that the possibility of a military strike are fading.
The rupee opened at 63.90 a dollar from the previous close of 63.84 on the interbank foreign exchange market and declined to a low of 64.20 as local stocks fell.
It rebounded to a more-than-three-week intra-day high of 63 before settling at 63.38, a rise of 46 paise or 0.72
In straight five sessions, the rupee has spurted by 425 paise or 6.28 per cent.
"The expectation that the Syrian crisis might not develop into a full-fledged war has led to the reduction in the safe-haven demand in the US dollar and Japanese yen. All the emerging nations currencies are seen benefiting," said Abhishek Goenka, CEO of India Forex Advisors.
Foreign institutional investors pumped in $421.15 million on Tuesday, according to data from the Securities and Exchange Board of India.
The benchmark S&P BSE Sensex stock index changed a little on Wednesday.
"Easing geopolitical tension in Syria is expected to stabilise global crude oil prices, which will help India to minimise the current account deficit," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
"The trading range for the spot USD-INR pair is expected to be within 62.80 to 64.30."
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