* Japan officials jawbone as dollar nears 160 yen

* Fed's favoured inflation index looms large this week

* US Presidential debate, French elections on horizon

SYDNEY/LONDON, June 24 (Reuters) - Global shares steadied on Monday ahead of U.S. price data that investors are banking on to show a renewed moderation in inflation, while markets were on alert for Japanese intervention as the dollar tested the 160-yen barrier.

Geopolitics also loomed large, with the first U.S. presidential debate on Thursday and the first round of voting in the French election at the weekend.

The MSCI All-World index rose 0.1% on the day, having fallen for the previous two sessions. In Europe, the STOXX 600 gained 0.5%, while U.S. index futures were up 0.1%.

Japan's Nikkei closed up 0.5%, with the continued decline in the yen putting pressure on the Bank of Japan to tighten policy despite patchy domestic data.

Minutes of the central bank's last policy meeting out on Monday showed there was much discussion about tapering its bond buying and raising rates.

Japan's top currency official Masato Kanda was out early to voice disapproval with the yen's latest drop which saw the dollar reach as high as 159.94.

The dollar was trading just a shade softer at 159.74, eyeing the 160.245 peak from late April where Japan is thought to have started spending around $60 billion buying the yen.

Demand for carry trades - borrowing yen at low rates to buy higher yielding currencies - has also seen both the Australian and New Zealand dollars reach 17-year peaks on the yen.

"Fresh cyclical highs for the dollar versus the yen overnight, further intervention jawboning from Japan's FX supremo Kanda and continued pressure on the yuan underline the pain being felt in Asia and EM more broadly from the Fed's high for longer stance, and will probably revive 'currency wars' chatter," Marc Ostwald, chief global economist at ADM Investor Services.

PARSING THE PCE

Even the euro was testing recent highs at 170.87 yen , despite being saddled with a round of soft manufacturing surveys (PMI). The euro is heading for a drop of 1.2% in June, its largest monthly decline since January. But on Monday, it was trading up 0.3% on the day at $1.0728.

"The decline in the euro area flash June PMI raises some concern that the nascent rebound is being cut short," analysts at JPMorgan wrote in a note.

"The abruptness of the drop is notable against the backdrop of the French election, which was mentioned explicitly by firms as a reason for the drag."

France's far-right National Rally (RN) party and its allies were seen leading the first round of the country's elections with 35.5% of the vote, according to a poll published on Sunday.

Manufacturing surveys from the United States, in contrast, showed activity at a 26-month high in June, though price pressures subsided considerably.

The latter shift whetted appetites for the personal consumption expenditures (PCE) price index due on Friday. Annual growth in the Federal Reserve's favoured core index is expected to slow to 2.6% in May, the lowest in more than three years.

"Note that low PCE deflator outcomes are needed to keep the y/y rate from rising through the course of this year given the string of low prints in the second half of 2023," cautioned analysts at NAB.

A low result would probably reinforce market bets on a Fed rate cut as early as September, which futures currently price as a 65% prospect.

There are at least five Fed speakers on the docket this week, including San Francisco Fed President Mary Daly and Fed Governors Lisa Cook and Michelle Bowman.

In commodity markets, gold pared losses in line with the retreat in the dollar to trade up 0.3% at $2,327 an ounce, while oil rose, pushing Brent crude up 0.4% to $85.57 a barrel and U.S. crude also up 0.4% at $81.00.

(Additional reporting by Wayne Cole in Sydney; editing by Muralikumar Anantharaman, Mark Heinrich and Sharon Singleton)