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FOREX-Dollar slips vs euro, sterling as ECB, BoE open door to hawks

* Sterling rises as BoE's Carney says a rate hike might be needed

* ECB's Draghi did not hint at immediate tightening-sources

* BOJ's commitment to easy policy supports greenback vs yen

TOKYO, June 29 (Reuters) - The dollar wallowed close to one-year lows against the euro and slipped against sterling in Asian trading on Thursday, as investors priced in tighter monetary policy in Europe.

The dollar index, which tracks the greenback against a basket of six major rival currencies, was steady on the day at 96.019, but well below highs above 97.0 hit earlier this week.

Sterling added to gains made after Bank of England Governor Mark Carney said on Wednesday that the central bank is likely to need to raise interest rates as the British economy comes closer to operating at full capacity.

European Central Bank President Mario Draghi sparked the euro's rally on Tuesday, when he hinted that the ECB could trim its stimulus this year.

The Federal Reserve hiked interest rates this month and left the door open for further increases later in the year, though a batch of mixed economic data recently has given investors' pause as to whether the Fed would be able to stay on its planned tightening path.

The dollar's decline "is broadly due to the reevaluation by market participants of the relative speed of the central banks to take away easing," said Bill Northey, chief investment officer at U.S. Bancorp Wealth Management in Helena, Montana.

"The ECB and the BoE might be moving more rapidly than before, and stubbornly low inflation in the U.S. might lead the Fed to revaluate its pace as well," he said.

The euro was slightly higher on the day at $1.13795 after scaling a peak of $1.13915 on Wednesday, despite evidence that positioning for a dramatic stimulus scale-back might have been overdone.

Draghi's remarks were intended to signal tolerance for a period of weaker inflation, not an imminent policy tightening, and set up September as the earliest the bank would discuss rolling back stimulus, according to sources familiar with the ECB chief's thinking.

The pound was up 0.1 percent at $1.2940 after spiking to $1.2971 on Wednesday, its highest since June 9.

The BoE's Monetary Policy Committee were split 5-3 earlier this month on whether to raise British interest rates from their record-low 0.25 percent.

By contrast, Bank of Japan policy members believed their best approach would be maintaining their current ultra-loose policy, with inflation well shy of their 2 percent target, according to a summary of the BOJ's latest meeting released on Monday.

The divergent monetary policy outlooks helped bolster the dollar against the yen, but it still edged down 0.1 percent to 112.28 after rising as high as 112.495 earlier in the session, its highest since May 17.

(Reporting by Tokyo markets team; Editing by Shri Navaratnam)