SINGAPORE (Reuters) -The dollar steadied on Thursday, after dipping alongside cooling U.S. inflation and falling bond yields, while the yen hit a one-month high on rising bets on a rate hike in Japan.

The yen was the biggest major mover against the dollar after softer-than-expected U.S. inflation data and it extended gains in Asia, as raised chances of Federal Reserve rate cuts coincided with murmurs of a Bank of Japan hike next week.

The yen traded as firm as 155.21 per dollar, its strongest since Dec. 19. It has gained about 1.2% in the last two sessions.

Recent remarks from BOJ Governor Kazuo Ueda and his deputy Ryozo Himino have made clear that a hike will at least be discussed at next week's policy meeting and markets see about a 78% chance of a 25 basis point increase.

"The fact that they are talking about hiking at this time, right ahead of the meeting may be testing the waters," said Bart Wakabayashi, branch manger at State Street in Tokyo.

The euro mostly held steady after the U.S. inflation data and was steady through the Asia day at $1.0283, while the dollar made small gains elsewhere and the dollar index snapped three days of losses to rise a little to 109.18.

There was little direct reaction in foreign exchange markets to the ceasefire deal in Gaza, though the Israeli shekel did touch a one-month high on Wednesday.

Core U.S. inflation was 0.2% month-on-month in December, in line with forecasts and below November's 0.3%. Annualised, the 3.2% reading was below expectations for 3.3%. That followed a similarly softer-than-expected British inflation reading and remarks from a Bank of England policymaker saying that the time was right to bring down interest rates.

Traders who have been growing worried about inflation responded with relief, buying stocks and sending benchmark 10-year Treasury yields down more than 13 basis points.

The currency reaction was a bit more muted and, besides the yen's gains, had begun to unwind on Thursday as traders kept a wary eye on still-strong U.S. economic readings and on possible tariffs along with Donald Trump's Jan. 20 inauguration as president.

"Of course, the dollar has overshot rate spreads lately," said Deutsche Bank macro strategist Tim Baker in a note. "But it's not all that large. The dollar should build in risk premium given the geopolitical backdrop.

"It's also completely normal to see dollar strength like this when U.S. growth is outperforming peers to this extent - and in previous episodes the dollar has overshot this relationship."

China's yuan, seen on the front lines of tariff risk, was pinned near the weak end of its trading band at 7.3316 throughout the Asia session. [CNY/]

The New Zealand dollar, at $0.5602, is not far from Monday's two-year low of $0.5543 and the Aussie received only the briefest boost from some robust jobs numbers.

It touched a week-high of $0.6248 in the moments after the data release but slid below $0.62 as the day wore on and remains within sight of Monday's five-year trough of $0.6131. [AUD/]

Sterling dipped 0.3% to $1.2212 and there was little relief for smaller currencies.

Indonesia's rupiah dropped to a 6-month low following Wednesday's surprise rate cut from Bank Indonesia.

South Korea's won, meanwhile, failed to see a boost from the central bank defying expectations for a cut to leave its benchmark rate on hold at 3% on Thursday.