The domestic currency had seen this level on July 22, 2015.
Intraday, the rupee hit a high of 63.55 against the American currency.
More From This Section
The current rupee rally has been spurred by sustained foreign fund inflows on expectations of more aggressive reform measures that will boost long-term economic growth against the backdrop of improving macro environment.
The local unit, however, held almost steady yesterday on speculation that the central bank may have intervened to counter its rise.
Breaching the psychologically significant 64-mark on Wednesday believed to have triggered stop-losses and panic unwinding as the sharp appreciation of the rupee has caught exporters on the wrong foot, a forex dealer said.
Heavy unwinding of long-dollar positions built by speculative traders last week ahead of FOMC meet also gave the rupee a boost, he added.
The greenback has been on the back foot throughout the week, largely impacted by uninspiring US economic data which have added to uncertainty about the pace of future Federal Reserve policy tightening amid political turmoil gripping Washington.
Meanwhile, heavy fag-end buying in select frontline counters along with short-covering bounces helped the domestic bourses to stage a smart rebound after their two-day slide.
Maintaining its strong edge against the beleaguered dollar, the Indian unit resumed modestly higher at 63.67 as compared to 63.69 Thursday at the Interbank Foreign Exchange market.
But, it soon slipped back to hit a fresh low of 63.73 briefly in mid-morning trade before rebounding to continue its northward journey.
After conquering yet another intra-day high of 63.55 towards the fag-end trade, the local unit finally settled down at 63.58, revealing a smart gain of 11 paise, or 0.17%.
For the week, it has strengthened by a solid 57 paise.
The RBI, meanwhile, fixed the reference rate for the dollar at 63.7091 and for the euro at 75.6609.
In cross-currency trades, the rupee gained further ground against the pound sterling to end at 83.56 from 83.75 per pound, but dropped further against the euro to finish at 75.48 from 75.44 earlier.
The domestic unit also weakened further against the Japanese yen to finish at 57.79 per 100 yens from 57.67.
In worldwide trade, the dollar struggled near its two-and-a-half year low against the euro and a seven-week trough versus the yen on Friday in the midst of sluggish US data also some caution ahead of closely watched non-farm jobs report later in the session.
The dollar index, which measures the greenback's value against a basket of six major currencies, rose about 0.20% to 92.87.
In forward market today, premium for dollar remained soft due to sustained receivings from exporters.
The benchmark six-month premium payable in January inched down to 138-140 paise from 139-141 paise and the far forward July 2018 contract also edged lower to 272-274 paise from 275-277 paise yesterday.
On the International commodity front, crude prices fell back after brief rebound with U.S. Crude remaining below the key USD 50-mar per barrel restrained by rising output from the United States as well as producer club OPEC.
US West Texas Intermediate (WTI) crude futures were at $48.93 per barrel in early Asian trade.
Brent crude futures, the international benchmark for oil prices, were at $51.90 a barrel, down 11 cents, or 0.2%, from their last close and around 70 cents for the week.