FOREX-Dollar in tight range as traders eye Middle East, US data

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* Investors monitor US-Iran talks, await key US economic data

* Federal Reserve policy outlook remains central to dollar direction

* Yen drifts toward 160 per dollar, heightening intervention risk

By Stefano Rebaudo

June 2 (Reuters) - The dollar traded in a tight range on Tuesday as investors watched for progress on a potential deal to reopen the Strait of Hormuz, while awaiting U.S. economic data later in the day, which could shape the Federal Reserve's policy path. A peace deal between the U.S. and Iran would ease pressure on currencies of oil-importing countries like Japan and the euro zone while curbing safe-haven demand for the dollar. U.S. President Donald Trump said on Monday that talks with Iran were ongoing, a move that prompted a drop in oil prices, despite a report also on Monday that Tehran had suspended indirect negotiations with the United States to end hostilities.

Investors have treated news of any progress toward ending the U.S.-Israeli war on Iran with caution, given the fragility of a ceasefire between Washington and Tehran struck in early April.

The dollar index, which measures the currency against six peers, was down 0.05% at 99.13. It has hovered in a narrow range of about 98.9 to 99.5 since May 15.

"By (Monday) evening, a sense of relief had returned as the U.S. president had seemingly secured another ceasefire in Lebanon," said Michael Pfister, foreign exchange strategist at Commerzbank.

"The foreign exchange market is nevertheless likely to be dominated by news of the situation today. But any news of setbacks in the negotiations will be met with considerable caution," he added.

The dollar had rallied at the onset of the Iran conflict, which began on February 28, buoyed by safe-haven demand and the U.S. economy's relatively limited exposure to energy-driven inflation. However, it has given back some of those gains due to the uncertainty of the war's trajectory.

DATA IN FOCUS Euro zone inflation data strengthened the case for a European Central Bank rate hike later this month, which markets had already widely anticipated. Traders increased slightly their bets on ECB hikes by December fully pricing two moves and an around 50% chance of a third hike.

The euro rose 0.12% to $1.1645.

"The pass-through of higher energy and input prices to final consumption will be limited due to a lack of ability and willingness of consumers to actually pay for these higher prices," Carsten Brzeski, head of macro at ING, said about the inflation outlook. Later, the U.S. Labor Department will release job openings data ahead of Friday's closely watched monthly employment report, with markets betting the U.S. central bank's next move will be to raise its benchmark interest rate.

"The combination of loose U.S. financial conditions, reversing safe-haven support and the Fed sounding patient has kept the dollar in check," Paul Mackel, global head of forex research at HSBC, said.

"However, a turning point is nearing, as much will increasingly depend on key economic data and what central banks say and do next, in particular the Federal Reserve," he added, pointing to the Fed's policy meeting scheduled in two weeks.

YEN'S 160 PER DOLLAR MARK IN THE SPOTLIGHT In Japan, Finance Minister Satsuki Katayama said on Tuesday the authorities stood ready to respond in the currency market as needed and refrained from commenting on recent exchange-rate moves.

The Japanese yen was a tad lower at 159.72 per dollar, close to the 160 level widely seen by markets as a trigger for intervention.

Markets are also waiting for a speech by Bank of Japan Governor Kazuo Ueda on Wednesday for possible signals as to whether the central bank will proceed with a rate increase next week. "But action remains likely, and even though inflation has eased, the risk of being behind the curve is rising," Derek Halpenny, head of research, global markets at MUFG, said.

(Reporting by Stefano Rebaudo and Satoshi Sugiyama; Editing by Neil Fullick, Emelia Sithole-Matarise and Chizu Nomiyama )