FOREX-Dollar stuck in narrow band as traders eye Middle East, US data

* 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 (Recasts lead, adds comments and background)

By Stefano Rebaudo and Satoshi Sugiyama

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 key 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 from 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, despite a report that Tehran had suspended indirect negotiations with the United States to end hostilities, a move that prompted a slight drop in oil prices.

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. Lebanon's announcement on Monday of a limited ceasefire between the Iran-backed Hezbollah and Israel also did little to give the market impetus.

The dollar index, which measures the currency against six peers, was down 0.05% at 99.05. 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.

US DATA IN FOCUS 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.

Friday's monthly U.S. employment report is expected to show a gain of 85,000 jobs in May and no change in the current 4.3% unemployment rate, according to a Reuters poll of economists.

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 against the dollar at 159.72 per dollar, close to the 160 level widely seen by markets as a trigger for intervention.

"If dollar/yen breaks above 160, the risk of surpassing the April 30 high would increase markedly, raising the likelihood of stronger verbal warnings and a renewed round of rate checks or actual intervention," said Mizuho Securities chief currency strategist Masafumi Yamamoto.

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 Shri Navaratnam, Neil Fullick and Emelia Sithole-Matarise)