* Inflation data seen key risk for FX markets this week
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh (Adds U.S. market open; changes dateline; previous LONDON)
NEW YORK, Sept 12 (Reuters) - The U.S. dollar on Tuesday clung to the previous day's gains, supported by a bounce in Treasury yields and ahead of U.S. inflation data that could influence the timing of the next Federal Reserve interest rate increase.
The greenback also found support as investors further unwound bearish bets against it. The dollar index, which tracks the currency against a basket of six major rivals, was up 0.05 percent at 91.92, after rising as high as 92.08.
The index rose 0.60 percent on Monday, its largest gain this month, as receding worries about North Korea and Hurricane Irma helped lift investor risk sentiment.
"Interest rates are certainly supportive of the dollar," said Erik Nelson, currency strategist at Wells Fargo Securities in New York.
U.S. long-dated Treasury yields reached two-week highs, rising for a third straight session amid a respite in geopolitical tensions in North Korea, with investors bracing for a 10-year note auction later in the session.
Short covering may have helped dollar notch gains against other major currencies, Nelson said.
An increasingly uncertain outlook for U.S. monetary policy and fiscal policy has taken a toll on the greenback this year, according to analysts.
Speculators have responded by boosting positions against the dollar to record levels in recent months.
Investor focus now turns to U.S. inflation data due on Thursday. The data is unlikely to show a significant pick-up in price pressures, with the August inflation reading forecast at 1.6 percent on an annual basis versus 1.7 percent in July. The Fed has a 2 percent inflation target.
"The U.S. inflation data is a big risk for the markets and given the extreme short dollar positioning in the market, the greenback may jump higher if inflation surprises on the upside," said Caxton FX analyst Alexandra Russell-Oliver.
Wells Fargo's Nelson said, however, said that, over time, there is still room for that positioning to get more short.
On Tuesday, the index pared gains slightly after the Labor Department said that job openings, a measure of labor demand, were little changed at 6.2 million in July.
Sterling rose against both the dollar and euro after UK inflation hit its highest in five years, adding to the case for the Bank of England to do more to support the pound.
The euro was up 0.02 percent against the dollar at $1.1953.
(Reporting by Saqib Iqbal Ahmed; Additional reporting by Saikat Chatterjee in London; Editing by Steve Orlofsky)