TOKYO (Reuters) - The dollar held on to most of its gains on Tuesday, following a sharp rebound on improving investor risk sentiment as worries over North Korea and Hurricane Irma receded.

FILE PHOTO: U.S. one hundred dollar bills are seen in this picture illustration, August 2, 2013. REUTERS/Kim Hong-Ji/Illustration/File Photo

The dollar index, which tracks the greenback against a basket of six major rivals, was steady at 91.874, after it skidded to a 2-1/2-year low of 91.011 on Friday.

The euro was little changed at $1.1955 after shedding 0.7 percent overnight. The common currency reached $1.2092 on Friday, its highest since January 2015, as the dollar suffered a broad retreat.

Higher U.S. Treasury yields also bolstered the dollar, as the benchmark U.S. 10-year note yield rose to 2.135 percent from its close of 2.125 percent on Monday, and 2.061 percent on Friday.

“Some people said the dollar’s fall and recovery was not strange, since U.S. yields got so low,” said Masashi Murata, currency strategist for Brown Brothers Harriman in Tokyo.

“But the market is still sensitive to risk-off news, maybe from North Korea, or from disappointing U.S. economic data,” he said. “So that’s why the dollar is still struggling to find its way.”

The dollar was steady at 109.39 yen after rallying 1.4 percent on Monday, its biggest one-day surge since mid-January. It had slumped to a 10-month low of 107.320 yen on Friday, when Hurricane Irma threatened Florida and as financial markets braced for the possibility of another missile or nuclear test to mark North Korea’s founding day on Sept. 9. The yen tends to benefit during times of economic and political uncertainty due to Japan’s net creditor nation status.

But Pyongyang’s anniversary passed without further tests, and Irma lost strength and was downgraded to a tropical storm after battering Florida over the weekend.

“Receding fear over Hurricane Irma and North Korea was a key factor behind the dollar’s bounce. Market focus is likely to return to fundamentals, although there aren’t many major events scheduled this week that could decide the direction for currencies,” said Shin Kadota, senior strategist at Barclays in Tokyo.

Major U.S. allies in Asia welcomed on Tuesday the U.N. Security Council’s unanimous vote to step up sanctions on North Korea, with its profitable textile exports now banned and fuel supplies to the reclusive North capped after its sixth nuclear test.

The Swiss franc, often sought in times of global risk aversion along with the yen, was flat at 0.9560 per dollar. The franc had rallied to a two-year high of 0.9421 on Friday.

The pound edged up 0.1 percent to $1.3175 after losing 0.25 percent on Monday.

Sterling fared better against the euro, brushing a fresh one-month high of 90.83 pence, aided by speculation that the Bank of England may sound more hawkish on interest rates in defence of the currency at its policy meeting on Thursday.

The Australian dollar was 0.2 percent lower at $0.8015, extending its retreat from a two-year peak of $0.8125 scaled on Friday.

The Chinese yuan pulled further away from Friday’s 21-month high against the dollar of 6.5432, after China’s central bank on Monday lifted measures put in place to support the yuan when it came under selling pressure.