By Francesco Canepa

WASHINGTON (Reuters) -European Central Bank policymakers are becoming increasingly confident about cutting interest rates in June as inflation continues its march lower, but there is little to no appetite for a big move, six sources told Reuters.

ECB governors gathering in Washington for the International Monetary Fund and World Bank's Spring Meetings took stock of a weakening economy in the euro zone and around the world as uncertainty from tariffs imposed by U.S. President Donald Trump puts a dampener on investment.

Data out of the euro zone also showed business growth stalling this month and pay hikes expected to ease considerably.

Most importantly for inflation, the 20% tariff rate provisionally imposed by Trump on European goods had been less severe than modelled by the ECB and the risk of retaliation by the European Union had so far been averted.

That meant that many governors were now seeing growing chances of an eighth quarter-point cut at their June 4 meeting, when the ECB will update its own economic forecasts. The ECB trimmed its benchmark rate to 2.25% earlier this month.

In line with the ECB's official line, they were keeping an open mind, however, given that the decision was still more than a month away and economic policy had become unpredictable since Donald Trump's April 2 announcement.

An ECB spokesperson declined to comment.

Trump's move shook investor confidence in the U.S. economy and even its status as the world's safe haven, causing fuel prices as well as the dollar to fall against the euro.

This resulted in growing disinflationary pressure in the euro zone, assuaging concerns about high price growth becoming entrenched among even some of the more hawkish members of the ECB's Governing Council.

The outlook further out remains foggy, however, with the prospect of a more fragmented world, cheaper imports from China and stronger domestic demand from Germany's fiscal spending plans creating contrasting forces.

For this reason, too, policymakers who spoke to Reuters saw no reason at present to consider a bigger, 50-basis-point cut, which they also believed might raise unnecessary alarm among market participants.

(Reporting by Francesco Canepa; Editing by Aidan Lewis)