Analysts in the poll were less optimistic about the rupee's prospects than they were in a similar poll last month, but said the currency is unlikely to weaken to the record low levels seen in August due to an improvement in the country's current account deficit.
The Chinese yuan, on the other hand, is expected to continue to slowly appreciate over the next year as the economy improves and on expectations that its central bank will widen the currency's trading band.
Median expectations from 20 strategists in the poll conducted this week were for the rupee to trade at 63 against the dollar at the end of February next year, weaker than its rate on Thursday.
It is then seen weakening further to 64.00 rupees per dollar by May and 63.43 rupees by November 2014.
"A tapering in the Fed's stimulus would drive the sentiment in the rupee in the near term along with domestic political clarity and fiscal management," said Shakti Satapathy, analyst at A.K. Capital Services in Mumbai.
"However, a good show on the current account deficit and other inflow driving measures from the government and Reserve Bank of India would restrict any sharp depreciation henceforth."
The U.S. Federal Reserve is expected to begin reducing its $85 billion a month bond purchases by March next year as its economy improves.
When that happens, rising bond yields in the U.S. will likely attract investors, boosting the dollar against emerging market currencies, which have been historically reliant on foreign exchange inflows.
In mid-May, when the Fed announced similar tapering intentions, most emerging currencies were dumped by investors leading to sharp falls in those currencies. The Indian rupee slumped 20 percent.
But recent data showed India's current account deficit has improved as the government and RBI rushed to put in place measures to stem the outflow of funds from the economy.
From increasing foreign direct investment limits on retail, telecom and aviation industries to curtailing gold imports and providing off-the-market swap windows for oil companies to buy dollars, the steps helped stabilise the rupee.
India's current account gap narrowed sharply in the September quarter to $5.2 billion or 1.2 percent of GDP -- the lowest since the June quarter of 2009.
Meanwhile, Finance Minister P. Chidambaram has vowed to lower the deficit to $60 billion for the fiscal year ending March 2014, counting on declining gold imports and double-digit export growth.
But analysts said risks remain.
"The only data which has improved is the current account deficit but it still continues to be a deficit and will widen from the current level of $5.2 billion per quarter," said Samir Lodha managing director at QuantArt Market Solutions.
Lodha says languishing economic growth, retail inflation of around 10 percent, an out-of-control fiscal deficit and looming elections were some of the factors that could threaten the stability of the currency.
General elections are due to be held in India by May next year and analysts said a hung parliament will adversely affect investor sentiment.
Despite its rebound in recent months, the rupee is still down about 11 percent for the year to date.
Meanwhile, the poll also showed the Chinese yuan will continue to rise slowly to 6.08 per dollar in three months, 6.05 by May next year and 6.00 by November.
It was trading at around 6.09 on Thursday.
Those predictions are slightly better than last month and signal expectations that the People's Bank of China will gradually widen its trading band as the economy improves.
The yuan has been the best performing currency in Asia so far this year, appreciating 2.3 percent.
The currency overtook the euro in October, becoming the second-most used currency in trade finance, global transaction services organisation SWIFT said on Tuesday.