* India's NSE gains as much as 0.75 pct to record high
* Rupee hits strongest vs dollar since Oct 2015
* Fed signals no pick-up in tightening, spurring gains
* But doubts remain abt sustainability of Indian rally (Updates with quote, details, background)
MUMBAI, March 16 (Reuters) - India's broader NSE share index hit a record high and the rupee rose to its strongest level in nearly 17 months on Thursday after the U.S. Federal Reserve signalled no pick-up in the pace of its interest rate tightening.
The gains, which tracked Asian markets, came after the Fed stuck to its outlook for two additional rate increases this year after lifting its overnight interest rate by 25 basis points on Wednesday as had been expected.
The tempered rate outlook knocked the dollar and eased worries of a fresh burst of capital outflows from emerging economies such as India. Some market watchers had recently speculated the Fed could hike rates four times this year as the U.S. economy gathers momentum.
The NSE index rose as much as 0.85 percent to a record high of 9,152.90 points, marking its second all-time peak in three sessions.
Sentiment had already been turning more bullish after a big election victory by Prime Minister Narendra Modi's ruling party in the key state of Uttar Pradesh at the weekend.
Hopes for sustained foreign flows into India have also sparked a rally in the rupee, which hit as much as 65.2250 per dollar, its strongest since Oct. 30, 2015.
Traders were split about whether the central bank had again intervened on Thursday to slow the gains, after stepping in the previous two sessions.
Meanwhile, the benchmark 10-year bond yield fell 5 basis points to 6.78 percent.
But the rally in markets has also raised strong doubts about its sustainability given concerns about share valuations and worries events such as upcoming elections in France will keep global flows volatile.
"I am a little concerned with this movement as I feel that the fundamentals of companies do not support this upward market movement (in shares). My expectation is that we may see a big correction of around 7-8 percent by April," said R.K. Gupta, managing director at Taurus Asset Management Company.
Foreign investors bought around a net $820 million in Indian shares in the two trading sessions after Modi's electoral win was announced.
Gains in share markets over this week have been widespread, with 45 out of 50 members in the NSE index rising on Thursday.
The NSE was up 0.6 percent as of 0500 GMT, while the benchmark BSE index was up 0.5 percent after earlier hitting its highest since March 2015
The rupee was last trading at 65.32/33 compared to its 65.71/72 close. (Reporting by Rafael Nam in MUMBAI and Arnab Paul in BENGALURU; Additional reporting by Swati Bhat; Editing by Kim Coghill)