NEW YORK, May 27 (Reuters) - The U.S. dollar, long stuck in a tight trading range, could be in for a break higher as the Federal Reserve shifts its focus to fighting worrisome signs that inflation is heating up.

In the first half of last year, the dollar slumped nearly 11%. Since then, it has settled into a narrow trading range, frustrating both those anticipating deeper losses and those hoping for a meaningful rebound.

Investors are eager to get the dollar's direction right, given the currency's pivotal role in global finance.

A softer dollar lifts profits for U.S. exporters by raising the value of repatriated foreign revenues. It also makes international assets more appealing to U.S. investors, who reap a currency tailwind on top of underlying asset returns.

The opposite is true when the U.S. currency strengthens. Imports from foreign countries can be cheaper in dollars unless tariffs are high enough to make up for it, while investments in other countries would return less when converted into dollars.

"If oil prices stay high and the Fed signals it's tightening, you could see the dollar strengthen further," said Thierry Wizman, global FX & rates strategist at Macquarie Group.

"I think there could be a little breakout," Wizman said.

The dollar index, which measures the U.S. currency's strength against a basket of six major peers, is up nearly 1.5% since February 27 - the day before the U.S.-Israeli strikes on Iran.

The dollar index last traded at 99.13, just below the 101 level which has marked the top of a five-point trading range for roughly a year.

Investors said a selloff in U.S. Treasuries has lifted yields, meaning the dollar could potentially generate higher returns. Investors also worry that higher oil prices triggered by the U.S.-Israeli war on Iran will fuel inflation.

Treasury yields have retreated somewhat in recent sessions as hopes for a breakthrough deal to reopen the Strait of Hormuz eased investors' inflation concerns, but yields remain well above pre-conflict levels.

The 10-year U.S. Treasury yield - a benchmark for mortgage rates and broader borrowing costs - has risen around 50 basis points since the start of the Iran war in late February. The 2-year yield, which tracks Fed rate expectations most closely and is the maturity most watched by currency traders, is up nearly 70 basis points.

Higher yields can boost the dollar's allure and investors see room for the U.S. currency to rise further.

Bond yields across Europe and Asia have also climbed. But the dollar is the currency used for trading on global oil and gas markets, and the U.S. economy has proved more resilient to the energy shock. This has given the dollar the advantage over rival currencies, particularly the euro.

"I think as long as the data justify spreads widening in favor of the dollar relative to Europe or Japan, the natural path for the dollar is to keep going up," Shahab Jalinoos, head of G10 FX research at UBS, said.

Even investors who hold a long-term bearish view on the dollar - citing structural concerns such as government deficits and rich valuations - have tempered that stance in the near term.

"Our stance has been on average negative dollar ... (but) tactically we've been sort of closer to neutral," said Ugo Lancioni, head of global currency at Neuberger Berman.

INFLATION FEARS

A key driver of the move in yields - which rise as bond prices fall - is an increase in inflation expectations fueled by higher oil prices. Rising inflation erodes the appeal of fixed-income instruments, prompting investors to demand higher yields.

"With no end to the crisis in sight, really, and with evidence of inflationary pressure actually feeding through into the data, it's becoming more and more difficult to look through that initial shock," said Oliver Shale, investment specialist for the U.S. at UK-based investment management firm Ruffer Investments.

Recent data have reinforced the view that price pressures are not easing as quickly as markets had hoped. Market-based measures of long-term inflation expectations, known as break-evens, rose to a three-year high of 2.508% on the benchmark 10-year note earlier this month and were last at 2.4%.

"Over the last handful of weeks we have tactically increased our dollar weight ever so slightly," Shale said, adding that longer term he remains skeptical of dollar strength.

FED WATCH

The new Fed Chair Kevin Warsh had long been expected to pave the way for rate cuts, but mounting inflation expectations have made that less likely.

"My baseline right now is that the Fed is going to move in a more hawkish direction in the next few weeks," Macquarie's Wizman said. The next FOMC meeting is scheduled for June 16-17.

The Iran war remains the biggest wild card, investors said. A lasting resolution would pose the greatest challenge to the dollar, simultaneously dampening inflation expectations and reducing safe-haven demand. For now, investors are reluctant to bet against the greenback.

"Who knows what happens on the geopolitical front, but the path of least resistance is, in our view, towards a stronger dollar against low-yielding currencies like the yen and the euro," UBS' Jalinoos said.