WASHINGTON, April 17 (Reuters) - The European Central Bank would be putting a dampener on the economy even after cutting interest rates twice, but there is no rush to slash borrowing costs, ECB policymaker Mario Centeno said on Wednesday.

ECB policymakers have unanimously come out in favour of reducing the policy rate from its current record high of 4% in June, but views diverge on the path beyond as some worry that inflation may prove sticky, as is happening in the United States.

In an exclusive interview with Reuters, the Portuguese governor said there was scope to cut rates and still have a "tight" stance -- central bank parlance for a level of borrowing costs that restricts economic activity.

"Even after 25 or 50 basis points of cuts we’ll still have a tight monetary policy stance," he said on the sidelines of the International Monetary Fund and World Bank Spring Meetings in Washington.

He described a first move in June as "very likely", after which he and colleagues will take their cues from incoming data, "particularly about unemployment and growth".

As for how far the ECB could cut, Centeno appeared to suggest the central bank bring rates down to 3%, but stressed there was no rush to do so.

"I don’t know anybody who says the neutral rate is above 3%," he said. "How fast should we get there? We’ve got time."

Centeno also dismissed market speculation about whether the ECB would hesitate to cut rates before the U.S. Federal Reserve, noting that output and investment were stagnating in the euro zone, unlike in the United States.

"We need to recognise that and conduct monetary policy according to euro zone data," he said. "If that means we need to cut interest rates before the United States, so be it. The number of times we cut will depend on the numbers that come in."

He said the ECB could deal with shocks that drove inflation higher, but argued that current shocks were actually deflationary, citing China's aggressive export policy as one. (Reporting by Francesco Canepa; Editing by Leslie Adler)