(Adds market details after close, adds SpaceX closing price)

* SpaceX surges after public debut

* Space stocks slide after rallying ahead of SpaceX debut

* Adobe drops after exit of CFO Dan Durn

* Indexes: Dow up 0.7%, S&P 500 up 0.5%, Nasdaq up 0.3%

By Caroline Valetkevitch and Johann M Cherian

June 12 (Reuters) - U.S. stocks ended higher on Friday as

investors held out hope for a peace deal between Iran and the

United States and as SpaceX shares surged in their debut, making

it Wall Street's biggest public listing in history.

The United States and Iran signalled that an agreement to end

their war was close, with a senior U.S. administration official

saying a draft proposal was in place that was liked by both

sides. U.S. President Donald Trump has said several times since

mid-March that a deal with Iran to end the war was close.

Market participants were glued to shares of Elon Musk's SpaceX

, which began trading on the Nasdaq on Friday. Its

shares closed up 19.2% at $160.95, well above the IPO price of

$135 apiece. Its market capitalization was last at $2.1

trillion.

Shares of other space stocks, which soared in the lead-up to

the debut, eased on Friday. Rocket Lab's ( RKLB ) stock fell

10.8%, while Intuitive Machines ( LUNR ) was down 13.1% and

Planet Labs declined 8.8%.

The reported progress in peace talks helped to lift

sentiment, said Jake Dollarhide, chief executive officer of

Longbow Asset Management in Tulsa, Oklahoma.

"There's still hope for a peace deal. Trump called off the

attacks ... Third parties are confirming a peace deal is

happening."

That puts pressure on oil prices and reduces worries about

higher inflation and interest rates, he said.

Investors were also looking ahead to next week's Federal

Reserve policy meeting, which will be the first under the

leadership of Kevin Warsh. Traders will be looking for any signs

of whether a rate hike is likely as fed funds futures traders

price in a 55% chance of an increase by December.

The Dow Jones Industrial Average rose 353.51 points,

or 0.70%, to 51,202.26, the S&P 500 gained 37.16 points,

or 0.50%, to 7,431.46 and the Nasdaq Composite gained

79.18 points, or 0.31%, to 25,888.84.

The small-cap Russell 2000 nabbed a record closing

high.

Stocks also ended higher for the week, with each of the

three major indexes up roughly 7% for the period.

But U.S. equity funds saw their first weekly outflow in three

weeks, and earlier this week the technology index

confirmed a correction. Analysts believe some of the recent

weakness could be due to traders trimming holdings ahead of

SpaceX's debut.

SpaceX is now ranked among the biggest publicly listed U.S.

companies.

Mike Dickson, head of research and quantitative strategies

at Horizon Investments in Charlotte, North Carolina, said he was

surprised by the lack of volatility in SpaceX so far, given the

hype around the IPO.

IPOs of AI companies OpenAI and Anthropic are also highly

anticipated later in the year.

SpaceX, which also includes Starlink and xAI, has already defied

some Wall Street conventions.

Some analysts have voiced caution, however, over the

fundamentals of the company, which posted more than $4 billion

in annual losses last year.

"Sentiment could easily turn sour because SpaceX is truly

overvalued at this level," Dollarhide said.

Shares of Tesla, another Musk company that trades at a

premium to its earnings, ended 1.8% higher.

On the flip side, Adobe slid 6.8% after the exit of CFO

Dan Durn.

Advancing issues outnumbered decliners by a 2.07-to-1 ratio

on the New York Stock Exchange. There were 372 new highs and 66

new lows on the NYSE.

On the Nasdaq, 2,678 stocks rose and 2,185 fell as advancing

issues outnumbered decliners by a 1.23-to-1 ratio. The S&P 500

posted 35 new 52-week highs and 10 new lows while the Nasdaq

Composite recorded 200 new highs and 112 new lows.

Volume on U.S. exchanges was 19.73 billion shares, compared

with the 20.7 billion average for the full session over the last

20 trading days.