Domestic bond markets have seen net inflows of more than $2 billion so far in January, although interest in stocks has been lacklustre with only around $258 million having come in so far in 2014, after investments of over $20 billion in 2013.
For the week, the unit rose 0.6 percent, its biggest weekly rise since the week to Dec. 4, after recent data showing easing wholesale and consumer inflation is reinforcing expectations the central bank will keep monetary policy on hold.
The Reserve Bank of India raised interest rates twice late last year to contain inflation, sparking concerns about declining economic growth.
"There was good selling seen from foreign banks. There is good flow coming in for the debt market investments," said Uday Bhatt, a foreign exchange trader with UCO Bank.
"I think next week too the pair should trade in narrow range between 61.25 to 61.75," he added.
The partially convertible rupee closed at 61.54/55 per dollar compared to 61.535/545 on Thursday. The unit rose as high as 61.3175 during the session, its strongest since Dec. 11.
Indian shares fell nearly 1 percent on Friday after Tata Consultancy Services slumped as its quarterly profit adjusted for other income lagged expectations, sparking some profit-taking in recently outperforming software services exporters..
Traders broadly see the pair holding in a 61 to 62 per dollar range until the central bank's monetary policy review on Jan. 28.
The U.S. dollar faded a little after a mixed bag of U.S. economic data, while the Australian dollar was vulnerable after disappointing jobs figures the previous day knocked it below an important support level to a 3-1/2-year low.
In the offshore non-deliverable forwards, the one-month contract was at 61.77 while the three-month was at 62.55.