The domestic currency had logged its previous best of 64.43 against the US dollar on June 19.
Heavy unwinding of dollars by currency speculators and banks in the midst of abundant capitals inflows predominantly supported the upmove.
The rupee resumed on a highly bullish note at 64.39 as against its overnight level of 64.54 at the Interbank Foreign Exchange (forex) market.
But, the local unit struggled to hold gains, quickly reverting an early spike and traded in a tight range for most part of the session before ending at 64.45, revealing a smart rise of 9 paise, or 0.14 per cent.
The rupee has recovered 14 paise in the last two days.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.4384 and for the euro at 73.7884.
Asian and emerging market currencies breathed a sigh of relief after Fed Chair Yellen expressed uncertainty about the effects of tightening on inflation and relayed a cautious outlook as investors re-calibrated their expectations for a slower pace of tightening in the US.
The dollar slipped against most of its trading peers.
Expectations that the US Federal Reserve will not tighten its monetary policy until the December meeting have largely helped emerging market currencies like rupee to gain, a forex dealer commented.
Meanwhile, basking in the glow of incessant record breaking journey, the flagship Sensex went past the impressive 32,000-mark for the first time ever and the broader NSE-Nifty closed at a new peak of 9,892 -- a few points shy of 9,900.
The Sensex zoomed over 232.56 points to close at a new peak of 32,037.38, while Nifty soared 75.60 points to settle at record high of 9,891.70.
The dollar index, which tracks the US currency against a basket of six major rivals, was little changed at 95.51.
In cross-currency trades, the rupee fell back against the pound sterling to settle lower at 83.28 from 83.05 per pound and also drifted further against the Japanese yen to close at 56.99 per 100 yens from 56.87 yesterday.
However, it recovered against the euro to conclude at 73.46 from 73.93 earlier.
In worldwide trade, the greenback remained under pressure amid uncertainty over the path of US monetary policy after the Federal Reserve lowered its interest rate projections.
The benchmark six-month premium payable in December eased to 136-138 paise from 137-139 paise, while the far forward June 2018 contract was quoted unchanged at 283-285 paise.
On the International commodity front, crude prices retreated on Thursday after the International Energy Agency (IEA) said the oil market could stay oversupplied for longer than expected due to rising production and limited output cuts by some OPEC exporters.
Brent crude fell 9 cents to USD 47.65 a barrel in early Asian trade.
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