The rupee had last ended at 67.22 per dollar on March 16, 2016.
The rupee continued its falling streak against the US currency for the third day, slipping by another three paise to hit 2-month closing low of 66.80 on persistent dollar demand from banks and importers on the back of higher greenback in the overseas market.
Rise in crude oil prices also affected the rupee-value against the dollar, a forex dealer said.
The rupee resumed lower at 66.90 as against the last weekend's level of 66.77 per dollar at the Interbank Foreign Exchange (Forex) Market and moved down to 66.91 on initial heavy dollar demand from banks.
However, it trimmed its initial losses and recovered 66.7225 per dollar before ending at 2-month closing low at 66.80, still showing a loss of 3 paise or 0.04 per cent.
The domestic currency has lost 24 paise or 0.36 per cent in the last three trading sessions.
The rupee had last ended at 67.22 per dollar on March 16, 2016.
The domestic currency hovered in a range of 66.7225 and 66.9100 per dollar during the day.
The dollar index was down by 0.0074 per cent in the late global trade against a basket of six global currencies.
Meanwhile, the RBI fixed the reference rate for the dollar at 66.8216 and euro at 75.5953.
In cross-currency trades, the rupee firmed up further against the pound sterling to finish at 95.99 from the last weekend's level of 96.27.
It also moved up further against the euro to 75.62 from 75.80.
However, the domestic currency ended unchanged against the yen at 61.32 per 100 yens.
The dollar was moderately higher against the yen in the late afternoon trade, with investors avoiding making major moves given a lack of fresh trading cues.
Investors are watching data and events this week, including January-March Japan gross domestic product data due Wednesday.
Tokyo-based dealers and analysts said a weak result will increase hopes that the government will implement extra stimulus to push up the dollar against the yen. The median forecast from a survey of 20 economists by the Wall Street Journal was for inflation-adjusted growth of 0.3 per cent.
Oil rose to fresh 2016 highs in Asia today as a slowdown in US drilling and increase in Chinese crude refinery processing bolstered hopes a supply glut would ease sooner than expected.
US benchmark West Texas Intermediate (WTI) for delivery in June was up 62 cents, or 1.34 per cent, at $46.83 a barrel. Brent North Sea crude for July was up 62 cents, or 1.30 percent, at $48.45.
Meanwhile, the Indian benchmark sensex ended higher by 163.66 points or 0.64 per cent to 25,653.23.
Pramit Brahmbhatt of Veracity Financial Services said, "Continuing weakness of previous day, the rupee opened on a negative note above 66.90/USD. But selling pressure in USD dragged it below the level. Strength in crude oil price governed rupee move, by putting pressure on it.
"Thus despite of gain in domestic equity market, we saw the rupee depreciating. The rupee closed with a loss of 3 paise at 66.80/USD. Trading range for spot USD/INR will be 66.50 to 67/USD."
In forward market, premium for dollar eased on persistent receivings from exporters.
The benchmark six-month premium for October moved down to 193.5-195.5 paise from the last weeeknd's level of 195-197 paise and far forward April 2017 contract also declined further to 399.5-401.5 paise from 401-403 paise.
