LONDON, May 31 (Reuters) - The dollar headed on Friday for its first monthly decline this year, ahead of key inflation data, after a downward revision to first-quarter U.S. economic growth suggested the Federal Reserve may still have room to cut interest rates this year.

The euro edged up after data showed price pressures in the euro zone picked up faster than expected in May, complicating the outlook for the European Central Bank.

Investors were awaiting the release of the Fed's preferred measure of inflation, the Personal Consumption Expenditures (PCE) price index, due at 1230 GMT, for further indications on how the central bank might proceed.

"The data-dependent Fed means that the April core PCE deflator will be an important market mover should it deviate away from the consensus 0.3% MoM (month-on-month) reading," said Chris Turner, head of markets at ING.

Official data showed on Thursday the U.S. economy grew at an annualised rate of 1.3% from January through March, down from the previous estimate of 1.6% after downward revisions to consumer spending.

The revision keeps the Fed on track to potentially cut rates at least once this year. The central bank will look closely at inflation data before it feels comfortable enough to begin cutting, analysts said.

Jim Reid, strategist at Deutsche Bank, said U.S. PCE data "still gets a lot of attention because it’s what the Fed officially targets".

Markets currently price in a 45% chance of a first rate cut in September, according to the CME Group's FedWatch Tool.

The dollar index fell 0.1% to 104.61, having hit a two-week high on Thursday. The index, which measures the performance of the U.S. currency against six others, is set for a drop of 1.6% in May, its largest monthly loss since December.

Earlier this month, softer U.S. consumer price inflation data rekindled rate cut expectations for this year, weakening the dollar across the board and setting it on track for its first monthly losses in 2024.

But expectations for rate cuts this year have wobbled amid signs of sticky inflation, most recently with a surprise uptick in consumer sentiment in data on Tuesday.

EURO ZONE INFLATION

The euro rose 0.2% to $1.0854. French inflation data released earlier on Friday, and German and Spanish figures earlier this week, all came in slightly higher than expected.

The numbers have not altered the view in markets that the ECB will cut rates when it meets next week.

According to all 82 economists polled by Reuters, an ECB rate cut on June 6 appears certain, with a majority predicting further reductions in September and December.

Elsewhere, the yen weakened, leaving the dollar up 0.2% at 157.16, but off this week's four-week high as Japan's finance minister repeated warnings about excessive currency volatility.

Data on Friday showed core consumer inflation in Tokyo accelerated in May, but price growth excluding the effect of fuel eased, heightening uncertainty over the timing of the Bank of Japan's next rate hike.

The yen has steadily slipped closer to the 34-year low of 160.245 from a month ago, a level which market players suspect triggered two rounds of dollar-selling intervention by Tokyo.

The offshore Chinese yuan was broadly steady versus the dollar at 7.2583 after an official factory survey showed China's manufacturing activity unexpectedly fell in May.

(Reporting by Joice Alves and Brigid Riley; Editing by Mark Potter and Mark Heinrich)