By Howard Schneider, Francesco Canepa and Leika Kihara

WASHINGTON/FRANKFURT/TOKYO (Reuters) -Top central banks continued with another round of interest rate hikes this week despite cooling inflation, but have now switched to a more cautious posture about further moves in a sign that a year-long round of global monetary tightening could be at an end.

The U.S. Federal Reserve and the European Central Bank delivered quarter-percentage-point rate increases this week, as expected, and left open the option of further hikes if inflation didn't continue a decline that has started to come faster than predicted on both sides of the Atlantic.

The Bank of England is expected to raise rates again next week following similar positive inflation news.

Meanwhile on Friday, the Bank of Japan opened the debate on plans to bring its ultra-loose policies to an end.

It has remained a dovish outlier by keeping rates ultra-low, but surprised markets on Friday by tweaking its yield control policy and allowing long-term borrowing costs to rise more, reflecting prospects of creeping inflation.

In Europe and the United States, a hike-first rhetoric has been common among top policymakers since last year.

But that has now been coupled with a broader view of how prices are evolving alongside the economy as a whole, a more comprehensive approach that could allow slower job and economic growth to serve as its own evidence that inflation will continue to fall.

That's a switch from policymakers' insistence over the past year that they needed to see actual declines in the pace of price rises to know progress was being made, and one that could inject what Fed Chair Jerome Powell described as a dose of patience into the debate over whether more rate hikes are needed.

The Fed's benchmark overnight interest rate now stands in the 5.25%-5.50% range, while the ECB's main rate is 3.75%.

"Given how far we've come, we can afford to be a little patient as well as resolute as we let this unfold," Powell said in a press conference on Wednesday following the Fed's decision to raise rates for the 11th time in its last 12 meetings.

"We want to see economic growth running at moderate or modest levels to help ease inflationary pressures. We want to see continued restoration of supply and demand balance, particularly in the labor market ... We see those pieces of the puzzle coming together."

'OPEN MIND'

For the ECB, President Christine Lagarde said a slight wording change in its latest policy statement was "not just random or irrelevant," but meant to communicate that after nine straight rate increases a pause would be on the table at the central bank's meeting in September, just as it will be for the U.S. central bank.

"We have an open mind as to what the decision will be in September and subsequent meetings," Lagarde said. "We might hike. We might hold ... I hope it is very clear that we are not in the domain of forward guidance."

New U.S. gross domestic product data on Thursday showed the path to a global pause is far from clear in an economy that continues to confound.

The economy grew at a faster-than-anticipated 2.4% annual rate in the second quarter, well above the 1.8% annual rate that Fed officials regard as the approximate trend consistent with their 2% inflation target. Yet quarterly inflation data came in weaker than expected.

While bond markets took a cue from the faster growth, and pushed yields on Treasuries higher, the days of coordinated global tightening may be numbered.

Though there was "material risk" inflation may still require further hikes, wrote Evercore ISI Vice Chairman Krishna Guha, "in the base case, the ECB - like the Fed - is done raising rates."

(Reporting by Howard Schneider; Additional reporting by Francesco Canepa and Balazs Koranyi in Frankfurt, and Leika Kihara in Tokyo; Editing by Dan Burns and Paul Simao)