Yellen on Wednesday said the US Central Bank has "more work to do" to help an economy and labour conditions that are still under-performing, while Rajan sought to temper concerns about India's own economy and about the threat posed by the return of dollar demand by oil companies into markets.
The comments have significantly eased nerves ahead of the wholesale price inflation data due on Thursday. Investors also believe the Reserve Bank of India under Rajan is giving increased focus to consumer prices as opposed to the wholesale data.
Rajan on Wednesday called food prices "worryingly high" but welcomed the falling core consumer inflation, while estimating the current account deficit would narrow to USD 56 billion this fiscal year from USD 87.8 billion the previous year.
Still, investors still remained cautious about whether the RBI can tackle the concerns about slowing economic growth after raising interest rates twice over the previous two month to tackle rising inflation.
"We are still skeptical regarding the rupee's fate, as it relates to the external deficit and the ability of the RBI to balance growth and inflation trade-offs," Sacha Tihanyi, senior currency strategist at Scotiabank in Hong Kong, said in a note.
The rupee rose to as high as 62.9525 to the dollar - its highest since Nov. 11, recovering after tumbling to a two-month low of 63.90 on Wednesday.
Benchmark 10-year bond yields were down 2 basis points to 8.90 percent, while shares gained more than 1 percent, heading for their first winning session in eight.

The gains marked a reversal in what so far been a tough week after stronger-than-expected US jobs data had sparked concerns about an early tapering of the Fed stimulus.

Those same fears had hit Indian markets badly when they first surfaced over the summer, sending the rupee to a record low of 68.85 to the dollar, although the currency has recovered 12.7 percent since then.
Investors are now awaiting the October wholesale price inflation data. A Reuters' poll of economists predicted headline inflation would accelerate to 6.90 percent from a 6.46 percent advance in September on the back of rising food prices.
Data on Tuesday had showed consumer price inflation accelerated more than expected, to 10.09 percent in October from 9.84 percent in September.
Still, prospects that the RBI would raise interest rates for a third time at its policy review in mid-December, after raising them by 50 basis points since September, are seen waning after Rajan's dovish comments on Wednesday.
The governor also sought to reassure investors worried about the rupee's stability after the RBI allowed oil companies to source dollars directly in markets instead of a special window provided by the central bank.
Rajan said the swaps entered by oil companies to repay the dollars borrowed would mature from February to April next year, and added the RBI would be able to manage any surge in demand on dollars at that time by rolling over some of the swaps or by settling them with net payments done in rupees.


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