The euro wavered in a narrow range on Thursday after the European Central Bank lowered rates from record highs after months of anticipation, ticking higher then briefly slipping with the outcome of the ECB meeting well priced in.

The euro was up 0.04% at $1.0872, not far from a two-and-a-half month top of $1.0916 hit earlier in the week. Against the yen the Japanese currency was up 0.10% at 169.895 yen.

The dollar index, which measures the greenback against a basket of currencies including the yen and the euro, gained 0.07% at 104.31, also in sideways mode with little reaction to a report showing that applications for unemployment benefits last week were more than expected at 229,000.

Inflation in the 20 countries that share the euro has fallen from more than 10% in late 2022 to just above the ECB's 2% target in recent months, largely thanks to lower fuel costs and a normalisation in supply after some post-pandemic snags.

But that progress has stalled recently and what had looked like the start of a major ECB easing cycle only a few weeks ago now appears more uncertain due to signs that euro zone inflation may prove sticky, as has been the case in the United States.

Now that the ECB cut is out of the way, the markets have turned their attention squarely on U.S. payrolls data on Friday.

"It was so much as expected, what ECB has said and done, that when you make the adjustments for the 25 basis point cuts right now the swaps market hasn't changed all that much," said Marc Chandler, chief market strategist at Bannockburn Global Forex in New York.

Chandler was referring to the euro zone/U.S. interest rate differentials that determine forward pricing for FX pairs and affect spot. He said that regardless it's not unusual for the dollar to weaken ahead of monthly employment release, then to rally back.

Until then, Thursday's talk is mainly about central banks. The Canadian dollar firming a little in the wake of Wednesday's expected Bank of Canada rate cut. The currency was last at C1.3686 per dollar.

Ahead of the U.S. jobs report, investors are grappling with the implications for the Federal Reserve of several pieces of U.S. data this week showing employment growth moderating, albeit along with a pick up in service sector activity.

The Federal Open Market Committee meets next week but is not expected to lower rates, yet. Markets are now pricing in nearly 50 basis points of Fed rate cuts this year, with the first most likely to come in September.

The euro was also 0.23% firmer on the pound at 85.18 pence though towards the bottom of its recent range.

Versus the dollar, sterling was down a whisker at $1.2779.

YEN RISES

The yen was firm at 155.96 per dollar, as investors digested Thursday remarks from Bank of Japan Governor Kazuo Ueda that it would be appropriate to reduce the central bank's bond buying as it moves toward an exit from massive monetary stimulus.

His comments come ahead of the BOJ's two-day monetary policy meeting next week.

"This was almost a momentum play from the Japanese central bank - that is, add in JPY positive news flow when funding currencies - JPY and CHF - were already being covered and bought back, and the result was the JPY rally gaining additional legs," said Chris Weston, head of research at Pepperstone.

The Japanese currency had a brief rally earlier in the week as investors unwound positions in yen-funded carry trades, following a strong election victory for Mexico's ruling party which sparked concern about disputed constitutional reform.

That resulted in a squeeze on long peso/short yen positions, which has been a favourite among carry trades.

In a carry trade, an investor borrows in a currency of a country with low interest rates and invests the proceeds in a higher-yielding currency

The peso was down fractionally against the yen, after a 2.6% gain in the previous session. It had fallen roughly 6% against the Japanese currency at the start of the week, in the wake of Mexico's election results.

In cryptocurrencies, bitcoin fell 0.38% to $71,024.00. Ethereum declined 0.8% to $3832.9.

(Reporting by Rae Wee; Editing by Christopher Cushing, Jacqueline Wong, Sriraj Kalluvila, Toby Chopra and Franklin Paul)