(Writes through, adds details, investor comment, updates prices)

* STOXX 600 down 0.3%, Wall St futures inch lower

* Dollar holds firm after spike in Treasury yields

* Yen hits fresh 40-year low; traders watch for intervention

* Oil falls as markets await outcome of Iran-US talks

By Danilo Masoni

MILAN, July 1 (Reuters) - World stocks edged lower on the

first day of the third quarter on Wednesday after a strong

rally, as investors awaited remarks from Fed Chair Kevin Warsh,

while softer euro zone inflation cooled bets on further interest

rate hikes.

Oil prices stayed near pre-war levels as investors weighed signs

that contacts between Iran and Washington aimed at reaching a

final deal to end their conflict were continuing.

Traders also watched for possible Japanese intervention after

the yen hit fresh 40-year lows against the dollar.

The MSCI World Price Index slipped 0.1% in

European afternoon trade after posting its strongest quarter in

around six years, up 13% on rallying chipmakers and tech stocks.

U.S. futures and European shares declined slightly.

"Iran is no longer a problem. There is no peace, but there

is no war either," said Carlo Franchini, head of institutional

clients at Banca Ifigest, saying he viewed another European

Central Bank interest rate hike later this month as unlikely.

Data backed that view. Euro zone inflation eased more than

expected in June, further reducing pressure on the ECB to raise

rates again after last month's first hike in nearly three years.

Inflation in the bloc slowed to 2.8% in June from 3.2% in

May, coming well below expectations for a 3.0% reading, as food,

energy and services price pressures all eased.

Traders marginally pared bets on further tightening after

the figures and were pricing in around 23 basis points of

additional ECB rate increases by year-end.

Europe's region-wide STOXX 600 was down 0.3% at 1120

GMT, steadying after a 10% quarterly rise that marked its

strongest performance since late 2020, with sentiment towards

the region helped in recent weeks by falling energy prices.

"The second quarter GDP data isn't going to be great. But

clearly prospects of the Strait of Hormuz (opening) and lower

oil prices is a major positive factor for Europe," said Kevin

Thozet, member of the investment committee at Carmignac.

AWAITING WARSH

Investors will be keen to hear what Warsh says when he

appears at the ECB's annual central banking forum in Portugal

for clues on the outlook for U.S. interest rates, ahead of

Thursday's key U.S. jobs data.

Warsh has long been against the Fed providing forward

guidance and may give little away on his policy intentions.

Lauren van Biljon, a senior portfolio manager at Allspring

Global Investments, said underlying inflation trends suggested

the Fed may not need to tighten policy further.

"If the energy price shock starts to roll off in the

month-on-month inflation numbers, and our U.S. analysts are

still pretty confident that shelter and rent are disinflationary

factors through to the end of this year, it looks like the Fed

will be on hold," she said.

Futures imply a 33% chance of a Fed rate hike at its

meeting later this month, while the probability of a September

move is priced at 67% to 88%.

The benchmark 10-year Treasury yield rose 4.9

basis points (bps) to 4.471%, while S&P 500 and Nasdaq

futures declined 0.1-0.3%.

Markets paused after Wall Street posted its strongest

quarter since 2020, driven by an 88% surge in the Philadelphia

Semiconductor Index.

With earnings season starting in mid-July, investors are

banking on strong tech results to justify lofty valuations and

continued inflows into the sector.

Goldman Sachs ( GS ) said the consensus is for earnings per share

to grow 22% from a year earlier, with AI infrastructure stocks

accounting for nearly 60% of that increase.

In Asia, Japan's Nikkei gained 0.6% after surging

37% last quarter, with strong tech demand lifting sentiment

among big manufacturers to an eight-year high.

South Korea's main index fell about 2%, following a

68% quarterly rally driven by AI-fuelled chip demand.

The rise in U.S. yields helped lift the dollar as high as

162.84 yen, a new four-decade high. The climb has drawn threats

of intervention from Tokyo, though authorities appear reluctant

to act, having spent almost 12 trillion yen ($74 billion)

through April and May to little lasting effect.

The euro was down 0.2% at $1.1394.

Germany's 10-year bond yield, the euro zone

benchmark, rose 2 basis points to 2.931%, while its two-year

bond yield, more sensitive to rate expectations, was

unchanged at 2.532% after the inflation data.

Brent crude was down around 1% at $72.27 a barrel,

reversing earlier gains, while gold was steady, trading

slightly above $4,000 an ounce after a difficult quarter.