Petrol prices were on Thursday cut by Rs 1.15 a litre, the second reduction in rates in a month, while diesel prices were raised by 50 paise per litre.
The price changes announced by oil companies are excluding local sales tax or VAT and will be effective from midnight, oil companies announced.
Petrol prices in Delhi will be cut by Rs 1.38 to Rs 71.02 per litre, while it will cost Rs 78.04 a litre in Mumbai as against Rs 79.49 currently.
The reduction comes on the back of a Rs 3.05 per litre (Rs 3.66 after including VAT) cut in rates effected from October 1.
Prior to that, petrol prices had since June risen seven times, totalling Rs 10.80 per litre, excluding VAT (Rs 13.06 after including state tax) as the rupee depreciated sharply against the rupee.
In a parallel move, diesel price was hiked by 50 paise, excluding VAT, in line with the January decision of the government allowing oil companies freedom to raise prices in small doses every month to wipe out mounting losses.
The diesel price in Delhi has been hiked by 56 paise to Rs 53.10 per litre while it would cost Rs 60.08 in Mumbai from Friday as compared to Rs 59.46 currently.
Thursday's hike is the 10th since the January 17 and most of the losses on diesel sales should have been wiped out by now to make the fuel market priced. But the fall in rupee, around 25% since April, has worsened the situation and losses mounted to Rs 14.50 per litre.
However, the recent firming of rupee against US dollar and monthly increases have trimmed these losses to Rs 9.58. Diesel rates have risen by a cumulative Rs 5.95 this year.
"Prices of petrol were last revised downwards on October 1 by Rs 3.05 per litre (excluding state taxes) on account of softening of prices in international markets as well as strengthening of the rupee.
"Since last price change, international prices of petrol have declined marginally from about $113 per barrel to about $112. The Rupee-USD exchange rate has appreciated from around Rs 63 to a US dollar to around Rs 62. Both these factors have resulted into a reduction in prices of petrol," Indian Oil Corp, the nation's largest fuel retailer, said in a statement.
IOC said exercising the January authorisation to increase the diesel prices within a small range every month, retail prices are being revised every month and today rates have been hiked by 50 paise per litre.
"Even after the current increase, under recovery (revenue loss) on retail diesel shall stand at Rs 9.58 per litre," it said.
Besides diesel, oil firms are losing Rs 35.77 per litre on sale of PDS kerosene and Rs 482.50 per 14.2-kg domestic cooking gas (LPG). These are lower than Rs 38.32 and Rs 532.50 loss incurred last month.
At current rates, IOC projected a revenue loss of Rs 71,200 crore on sale of diesel, domestic LPG and kerosene for the full 2013-14 fiscal. The industry (IOC plus other state fuel retailers HPCL and BPCL) are projected to incur an under recovery of Rs 135,900 crore.
"The movement of prices in international oil market and Rupee-USD exchange rate is being closely monitored and developing trends of the market will be reflected in future price changes," the statement added.