MUMBAI, Sept 20 (Reuters) - The Indian rupee firmed on Tuesday as the dollar retreated on improving risk sentiment, with investors assessing just how hawkish the Federal Reserve would be at its policy meeting over the next two days.

The partially convertible rupee rose 0.2% to 79.61 per dollar by 0508 GMT. It has weakened 0.8% in the past four sessions from a high of almost 79.10.

"There will be some breather for the rupee. It may trade around 79.45-79.80 before the Fed event as we'll see more of a consolidation phase," said Kunal Sodhani, vice president at global trading centre, Shinhan Bank.

Asian equities jumped, tracking their U.S. counterparts, with Indian stocks outpacing peers to climb 1.3%. Currencies in the region, though, remained subdued due to the yuan's continued weakness.

The dollar index slipped 0.1% to 109.6.

Treasury yields continued to firm, with the 10-year yield reaching its highest level in more than a decade. The two-year yield was within a few basis points of the key psychological 4% level.

Investors are preparing for another 75 basis points rate hike by the Fed on Wednesday, which has been fully priced in, but there is an outside chance of a 100 bps increase. Odds of that have, however, come off from the peak of near 40% to under 20%.

Markets are worried rates would be kept higher for longer to control inflation, which could tip the U.S. economy into a recession and have ripple effects on the broader global economy.

"But if the Fed is not as hawkish as markets are expecting, particularly in their long-term view, the dollar index will come off. So looking at their dot plot for interest rates and commentary on inflation will be key," Sodhani added. (Reporting by Anushka Trivedi in Mumbai; Editing by Savio D'Souza)