Oil prices have been making some headlines recently, triggering near-term worries that expensive oil may lead to a fiscal slippage and stoke inflation.
In a fiscally constrained environment, rising import bill can put further downward pressure on the rupee, a forex dealer commented.
Meanwhile, crude prices flared-up to cross above the USD 68-mark a barrel briefly - its highest since May 2015 largely supported by OPEC-led production cuts and falling US crude inventories.
Brent crude, the international benchmark, was trading higher at USD 67.99 a barrel in early Asian trade.
Foreign portfolio investors (FPIs) were net buyers and bought shares worth Rs 6928.3 million yesterday.
Meanwhile, direct tax collection rose 18.2 per cent for the April-December period of the current fiscal to Rs 6560 billion in advance tax mop up, the finance ministry said.
The net collections represent 67 per cent of the total Budget estimate of Rs 9800 billion for 2017-18.
In the meantime, Indian bourses continued their record breaking run for the third straight day driven by sustained foreign funds buying amid expectations for robust Q3 earnings.
Asian stocks were mixed in a session, which saw no huge moves either way.
The benchmark Sensex rose 90 points to end at a new peak of 34,443.19, while Nifty added 13 points to record high of 10,637.
Staging a recovery from fresh 2018 low, the rupee resumed modestly higher at 63.48 compared to Monday's close of 63.51 at the Interbank Foreign Exchange (forex) market on fresh dollar selling by exporters and banks amid early gains in domestic stocks.
It gained further ground to hit an intra-day high of 63.43 in mid-mornings deals before succumbing to fresh dollar pressure.
After touching a low of 63.73 towards the tail-end session, the local unit ended the day near its lows of 63.71, a loss of 20 paise, or 0.31 per cent.
The rupee had strengthened 55 paise since the start of 2018.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 92.25 in early trade.
Globally, the dollar was hovering at one-week high against other major currencies on expectations for rate hikes after San Francisco Fed President John Williams said that the Fed should raise interest rates three times this year given that economy will benefit from tax cuts.
In cross-currency trades, the rupee continued to slip against the pound sterling to end at 86.23 per pound from 85.96 and the Japanese yen also declined further to close at 56.52 per 100 yens from 56.13 earlier.
The rupee, however, remained firm against the euro to finish at 75.97 compared to 76.15.
In forward market today, premium for dollar displayed a steady to firm trend.
The benchmark six-month premium payable in June was stable at 132-134 paise, while the far forward December 2018 contract edged up to 270-272 paise from 268.50-270.50 paise yesterday.