Updates to afternoon trading, adds analyst comment and market details

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 SPCX.O, 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.O fell 8%, Intuitive Machines LUNR.O dropped 12.5% and Planet Labs PL.N shed 9%, while funds holding shares of SpaceX such as Fundrise Innovation Fund VCX.N 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 .DJI rose 351.73 points, or 0.69%, to 51,200.65, the S&P 500 .SPX gained 23.84 points, or 0.32%, to 7,418.14 and the Nasdaq Composite .IXIC 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 .SPRLCT confirmed a correction. Analysts believe some of the weakness in U.S. stocks and bitcoin's BTC= 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 TSLA.O, 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 ADBE.O 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.