Updates at 0530 GMT

By Ankur Banerjee

SINGAPORE, July 1 (Reuters) -Uncertainty over the U.S. rates outlook kept Asian shares steady on Monday, while the euro rose after the first-round voting in France's shock snap election was won by the far-right, albeit with a smaller share than some polls had projected.

The shock vote has unsettled markets as the far-right, as well as the left-wing alliance that came second on Sunday, have pledged big spending increases at a time when France's high budget deficit has prompted the EU to recommend disciplinary steps.

On Monday, the euro EUR=EBS was 0.41% higher, while European stock futures STXEC1 rose 1.4% and French OAT bond futures FOATc1 gained 0.15% as investors digested the better than feared results, although uncertainty remained.

"There is a sense of relief that the first round of the French elections weren’t as comprehensively in Le Pen’s favour as the polls indicated," said Tony Sycamore, market analyst at IG.

"This raises hopes that National Rally won't win an outright majority, nor be in a position to open the purse strings, a proposition which had the French bond market and the euro looking nervously over their shoulders."

Exit polls showed Marine Le Pen's National Rally (RN) winning around 34% of the vote, comfortably ahead of leftist and centrist rivals but the chances of eurosceptic, anti-immigrant RN winning power next week will depend on the political dealmaking by its rivals over the coming days.

The focus now shifts to next Sunday's runoff and will depend on how parties decide to join forces in each of France's 577 constituencies for the second round, and could still result in a majority for RN.

"Investors are concerned that if the far-right National Rally party wins a majority, this could set the stage for France to clash with the EU, which could disrupt Europe’s markets and the euro sharply," said Vasu Menon, managing director of investment strategy at OCBC.

In Asia, the MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS was 0.04% lower, in a subdued start to the second half of the year having risen 7% so far in 2024.

China stocks were mixed, with blue-stocks .CSI300 down 0.19% and the Shanghai Composite index .SSEC up 0.31% after a mixed set of data.

Factory activity among smaller Chinese manufacturers grew at the fastest pace since 2021 thanks to overseas orders, while weak domestic demand and trade frictions had led to another industrial sector contraction.

On the macro side, the spotlight remains on if and when the Federal Reserve will start cutting rates in the wake of data on Friday showing U.S. monthly inflation was unchanged in May.

In the 12 months through May, the PCE price index increased 2.6% after advancing 2.7% in April. Last month's inflation readings were in line with economists' expectations but they remain above the Fed's 2% target for inflation.

Still, markets are clinging to expectations of at least two rate cuts from the Fed this year with a cut in September pegged in at 63% probability, CME FedWatch tool showed.

Investor focus this week will be on the minutes of the Fed's June meeting that will offer more clues on the central bank's thinking before the spotlight switches to payrolls data on Friday. The Feb in June projected just one rate cut in 2024.

Among currencies, the yen JPY=EBS traded slightly weaker at 161.06 per dollar after skidding to 161.27 on Friday, its weakest level since late 1986, keeping traders on edge for signs of intervention from the Japanese authorities.

A quarterly central bank survey showed on Monday the business mood in Japan's service sector soured in June, while a rare unscheduled downgrade to the country's GDP data also showed the economy shrank more than reported in the first quarter.

The euro touched a more than two week high of $1.076175 in early Asian hours, pushing the dollar index =USD, which measures the U.S. unit against six rivals, a touch lower at 105.61.

In commodities, oil prices edged higher, with Brent futures LCOc1 0.39% higher at $85.33 per barrel and U.S. West Texas Intermediate crude futures CLc1 up 0.39% at $81.86. O/R

Editing by Stephen Coates and Miral Fahmy

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