* Wall Street follows European stocks higher after Asian

markets rally

* President Trump says peace deal could be signed this

weekend

* Investors wait for Iran-U.S. deal details

* Record-breaking SpaceX IPO could help set the tone for

markets

(Updates prices to U.S. morning trading)

By Sinéad Carew and Iain Withers

NEW YORK/LONDON June 12 (Reuters) - MSCI's global equities

index rose on Friday and oil prices fell on fresh hopes for a

peace deal between Iran and the U.S., while investors awaited

the hotly anticipated market debut of Elon Musk's SpaceX

.

Stocks had rallied sharply on Thursday after U.S. President

Donald Trump said the countries were close to a deal. But, on

Friday, terms of a proposed memorandum to end the war in the

Gulf outlined by Western, Pakistani and Iranian sources on

Friday appeared to strongly favour Iran, drawing criticism from

Trump, who called the reports inaccurate.

Meanwhile, Iranian Foreign Minister Abbas Araqchi said that

an "Islamabad Memorandum of Understanding" for addressing the

U.S.-Israeli war on Iran had "never been closer", but urged

media outlets to refrain from speculating about its contents

until it was finalised.

U.S. Treasury yields rose while the dollar edged up in

morning trading while stocks climbed back up from morning

declines. While investors were hopeful for Middle East progress,

Chris Zaccarelli, chief investment officer at Northlight Asset

Management, said they were anxious for details.

"You never know what the final details will be. You never know

which side has the whole story. That's what markets have been

really grappling with, not knowing who to believe," said the

money manager who added that after the "really large pop" on

Thursday, some investors were taking profits on Friday.

Trump has repeatedly said a deal with Iran to end the war

was close since mid-March. This time, the indication that

diplomacy was continuing productively was enough for the market

to latch on to, Michael Nizard, head of multi-asset at Edmond de

Rothschild Asset Management, said, "Today, I think the

(potential for) peace is well under-priced."

Northlight's Zaccarelli noted that Friday's other main focus

for the market is the SpaceX IPO, which raised a record $75

billion, valuing the rocket and spacecraft manufacturer at $1.77

trillion and making Musk the world's first trillionaire.

"It's a barometer for overall risk appetite and the health

of the market in general. So generally speaking, a positive

result on this specific IPO because it's so large and so high

profile, does bode well for the broader market," he said.

On Wall Streetat 10:45 a.m. ET (1445 GMT) the Dow Jones

Industrial Average rose 225.95 points, or 0.45%, to

51,075.77, the S&P 500 rose 4.13 points, or 0.06%, to

7,398.43 and the Nasdaq Composite fell 69.72 points, or

0.28%, to 25,736.91.

MSCI's gauge of stocks across the globe

rose 8.91 points, or 0.81%, to 1,108.46.

The pan-European STOXX 600 index rose 1.46%. The

European Central Bank had to raise interest rates for the first

time in nearly three years on Thursday to nip war-driven

inflation in the bud. Final inflation data from several European

countries including France and Spain showed inflation

accelerated in May, while official data showed Britain's economy

contracted by 0.1% in April - its first monthly drop since

August.

In energy markets, oil futures were adding to Thursday's

losses. U.S. crude fell 1.45% to $86.44 a barrel after

touching its lowest level in almost two months. Brent

fell to $89.19 per barrel, down 1.32% on the day after earlier

falling to its lowest level in three months.

In fixed income markets, U.S. Treasury yields rose from

one-week lows as traders also looked ahead to next week's

Federal Reserve policy meeting, which will be first under the

leadership of Kevin Warsh.

In currencies, the dollar index, which measures the

greenback against a basket of currencies including the yen and

the euro, rose 0.05% to 99.78, with the euro down 0.05%

at $1.1571.

Against the Japanese yen, the dollar strengthened

0.21% to 160.25. Traders are still on high alert for

intervention from Japanese authorities as the yen stays close to

the 160 level that many see as a line in the sand.

In precious metals, spot gold fell 0.71% to $4,183.92

an ounce while spot silver fell 1.3% to $66.48 an ounce.