(Updates to afternoon trading, adds analyst comment and market

details)

* 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 0.3%, Nasdaq up 0.1%

By Caroline Valetkevitch and Johann M Cherian

June 12 (Reuters) - U.S. stocks were modestly higher on

Friday afternoon 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 were last up 27.9% at $172.55, well above the IPO price

of $135 apiece, valuing the company at more than $2 trillion.

Shares of other space stocks, which have soared in the

lead-up to the debut, eased on Friday. Rocket Lab ( RKLB ) fell

8%, Intuitive Machines ( LUNR ) dropped 12.5% and Planet Labs

shed 9%, while funds holding shares of SpaceX such as

Fundrise Innovation Fund rose 1.3%.

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.

"We might see a little drift up all day as you don't have

the sellers and you might entice a few more buyers in," he said.

The Dow Jones Industrial Average rose 351.73 points,

or 0.69%, to 51,200.65, the S&P 500 gained 23.84 points,

or 0.32%, to 7,418.14 and the Nasdaq Composite gained

28.41 points, or 0.11%, to 25,837.58.

Investors were also looking ahead to next week's Federal

Reserve policy meeting, which will be the first under the

leadership of Kevin Warsh.

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 weakness in U.S. stocks

and bitcoin's 16% fall last week could be due to traders

trimming holdings ahead of SpaceX's debut.

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

companies.

Shares of Tesla, another Musk company that trades at a

premium to its earnings, were up just 0.7%.

Only about 3% to 4% of SpaceX's shares are expected to be

available for trading, with a large allocation to retail

investors.

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. Index providers such as Nasdaq and

FTSE Russell have tweaked their entry requirements for its

inclusion, while the company also set its stock price at $135,

even before the roadshow began, reflecting Musk's sway over the

IPO.

Some analysts have voiced caution, however, over the

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

in annual losses last year.

Among the day's decliners, Adobe slid 7.8% after the

exit of CFO Dan Durn.

Advancing issues outnumbered decliners by a 2.18-to-1 ratio

on the New York Stock Exchange. There were 338 new highs and 60

new lows on the NYSE.

On the Nasdaq, 2,730 stocks rose and 1,999 fell as advancing

issues outnumbered decliners by a 1.36-to-1 ratio.