UPDATE 3-ECB firmly behind June rate cut but views diverge on July

(Adds comments by ECB board member Schnabel in paragraphs 9-11)

WASHINGTON/FRANKFURT, April 17 (Reuters) - European Central Bank policymakers continued to line up behind a June interest rate cut on Wednesday despite rising oil prices and a weaker euro, but they diverged on the path for monetary policy beyond the initial move.

The ECB has flagged a rate cut for June 6, but policymakers have largely avoided discussing what happens later on, partly on uncertainty over prices and partly due to risks that the U.S. Federal Reserve, which sets the tone for the world economy, could delay its own rate cuts.

Bundesbank chief Joachim Nagel fully backed the June move but ECB board member Piero Cipollone also appeared to entertain another move later on.

"If we see that the incoming data, and we'll receive many data in July and June ... will confirm our confidence that inflation is really (moving) to target, it will be appropriate to remove some of the restriction that we put in place," Cipollone told the IIF forum in Washington.

Greek central bank chief Yannis Stournaras and Lithuania's Gediminas Simkus have both suggested that July could be in play while others, including ECB Chief Christine Lagarde, have pushed back on any talk beyond the June 6 meeting.

Nagel was also cautious.

"If prices and the economy develop as expected, I would support a cut in key interest rates in June," he told German magazine Wirtschaftswoche.

"However, the latest data from the U.S. reminds us that the return of inflation to the target is not a surefire success. It is therefore right that the ECB Council has not committed itself to a rate cut in June," Nagel said.

ECB board member Isabel Schnabel, also a German, stressed she and her colleagues should take official forecasts for inflation to fall to 2% and stay there with a pinch of salt, and consider scenarios in which it does not.

"In an alternative scenario, productivity growth would remain depressed over the projection horizon and demand for less interest-rate sensitive services could remain sufficiently strong," she told an event in Washington.

"Overall, in this scenario, underlying price pressures could be stickier and the return of inflation to the 2% target delayed."

Markets now see just three rate cuts from the ECB this year, most likely in June, September and December, a big retreat from two months ago when between four and five moves were expected.

Both Cipollone and Nagel said that commodity prices were a key risk and added to the uncertainty since the euro zone was a big importer of energy.

Still, Cipollone, the newest member of the ECB's Executive Board, repeated the bank's most recent message that inflation rates could hover near their current level - 2.4% in March - before falling to the ECB's 2% target in 2025.

He also said that the recent drop in productivity, a big concern for economists, could reverse once the recovery takes hold.

Some argue that productivity fell sharply because firms have been hoarding labour in a quasi-recessionary environment and this will mechanically unwind as the initial phase of growth is unlikely to be accompanied by a further rise in employment. (Reporting by Francesco Canepa and Balazs Koranyi; Editing by Alex Richardson and Toby Chopra)