By Rae Wee and Kevin Buckland

SINGAPORE/TOKYO, Sept 1 (Reuters) - The dollar rose broadly on Thursday, particularly against the yen, as investors braced for higher U.S. interest rates while expecting anchored Japanese rates to go nowhere anytime soon.

The greenback hit a 24-year high of 139.59 against the yen in early Asia trade, a gain of about 0.5% on the previous day's close.

Expectations for a 75-basis-point U.S. rate hike at next month's Federal Reserve meeting are rising on the back of solid economic data, with Fed funds futures last pointing to a 73% chance of such an increase.

"Dollar/yen should break 140 before the September (Fed meeting). Looks like we won't have to wait much longer," said Sean Callow, a currency strategist at Westpac in Sydney.

"So long as expectations for the peak in the Fed funds rate keep ratcheting higher while the Bank of Japan remains on hold, dollar/yen will be a buy on dips. Anywhere in the low 140s now looks plausible."

Sterling fell about 0.4% to a new 2-1/2 year low of $1.1576, as clouds gather over the British economy. The euro fell 0.3% but was clinging on above parity at $1.0022 as red-hot inflation stokes hike bets in Europe.

Euro zone inflation rose to a record high at 9.1% in August, data released on Wednesday showed, solidifying the case for further big European Central Bank (ECB) rate hikes to tame inflation.

Markets have priced in about a 40% chance the ECB will increase rates by 75 basis points next week, even as risks of a painful recession rise along with gas prices.

"The high inflation and gas supply are still major issues in both the eurozone and the UK, and I think it's going to keep downward pressure on both those currencies," said Joseph Capurso, head of international economics at Commonwealth Bank of Australia.

"I can see the euro going back below parity again quite soon."

The U.S. dollar index, which measures the greenback against a basket of currencies, was up 0.12% to 108.99 in early Asia trade, not far off its two-decade high of 109.48 hit on Monday.

"The U.S. dollar has a bit more upside, partly because we think the market is underestimating how high the Federal Reserve could take the funds rate," said CBA's Capurso.

Yields on U.S. Treasuries rose accordingly. The two-year Treasury yields were up at 3.516%, the highest since late 2007, while expectations for the peak in the Fed funds rate crept closer to 4%.

The risk-sensitive Australian and New Zealand dollars were under pressure, with the Aussie down 0.3% at $0.6821, while the kiwi fell 0.3% to $0.6102.

(Reporting by Rae Wee; Editing by Ana Nicolaci da Costa)