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The Indian central bank's simultaneous purchase and sale of U.S. dollars in recent weeks has puzzled bankers, who speculate there may be multiple objectives behind the operations.

The Reserve Bank of India (RBI) has been buying dollars amid hefty foreign inflows, and has, at the same time, been selling them to prevent the rupee breaching its record low, several traders said.

Overseas investors have pumped in $3.7 billion into Indian equities and $800 million into debt in the six sessions in December, according to the National Securities Depository.

Still, the rupee is nearly unchanged month-on-month and has traded in a narrow 15-paisa range.

The currency's inability to appreciate points to the RBI absorbing the inflows, several traders and treasury officials said.

"It has to be the RBI (absorbing the flows)," a senior treasury official at a large private sector bank said.

"The price action and what I see on the screen clearly point to the RBI," this person said, referring to the heavy buying interest and the smallest of dips in the dollar/rupee not sustaining.

The RBI did not immediately respond to an email by Reuters seeking comment.

The rupee was at 83.38 to the dollar on Tuesday, just shy of its lifetime low of 83.42.

The unit has been trading near its record low despite expectations the Federal Reserve will cut rates as soon as March next year.

Meanwhile, Asian peers have rallied.

"It's puzzling - RBI's heavy both-side intervention," head of proprietary FX trading at a bank said.

On the one hand, the RBI is selling dollars to make sure the rupee does not weaken and at the same time it is "absorbing any kind of downward draft (on USD/INR)," this person said.

It's a "peculiar kind of strategy" that the RBI is following which has left the market confused, Abheek Barua, chief economist at HDFC Bank said.

"The way I can rationalize it is by thinking in terms of FX reserves and that of rupee liquidity," Barua said.

RBI's forex market intervention has several implications beyond the dollar/rupee rate.

Buying dollars flowing into the local market boost India's forex reserves and add to the rupee liquidity in the banking system. Selling dollars does the reverse.

India's FX reserves have climbed to a more-than-four-month high of $604 billion, data released last Friday showed.

Banking system liquidity, which was in a large deficit in November, has moved to a surplus in December.

The RBI reinforcing its "low volatility regime" for the rupee and the currency's overvaluation could also be reasons for the simultaneous buying and selling of the dollar, the treasury official at the private bank said.

According to the RBI's latest monthly bulletin, the rupee was overvalued by about 5% against a basket of 40 currencies.