(Adds close of U.S. markets)
* Trump says Tehran 'standing down' after missile attack
* Global equity index, stocks on Wall Street rebound
* Oil, gold prices tumble after spiking on Iran strike
By Herbert Lash
NEW YORK, Jan 8 (Reuters) - Oil prices tumbled and equity markets soared on Wednesday after U.S. President Donald Trump said an Iranian missile strike on bases in Iraq had not harmed American troops and damage was minimal, showing Tehran wanted to de-escalate the Middle East standoff.
Iran fired missiles at military bases housing U.S. troops in Iraq in retaliation for last week's slaying by American drones of Iranian Major General Qassem Soleimani, a strike that raised fears of an escalating regional conflict.
"Iran appears to be standing down, which is a good thing for all parties concerned and a very good thing for the world," Trump said in an address to the nation.
The S&P 500 and Nasdaq stock indexes hit record highs after Trump's remarks and crude prices slumped, with U.S. benchmark West Texas Intermediate posting a 10% slide from a peak following the Iranian attack to after Trump spoke.
Gold had surged past $1,600 for the first time in nearly seven years in earlier trade before discarding gains as fears of a larger conflict abated, leading investors to move out of safe-haven assets as risk appetite returned.
The safe-haven yen fell from three-month highs against the dollar and the Swiss franc, another safe haven, also retreated. Brent oil futures slid off a four-month peak hit in frenzied early trade soon after the Iranian attack.
"Once Trump spoke and suggested that this is basically done for now, risk took off. We're back to the all-time highs in the S&P and accordingly so-called safe assets sold off," said Jacob Oubina, senior U.S. economist at RBC Capital Markets.
Iran's long-term goal of a sphere of influence might be jeopardized if it attacks too aggressively, said John Vail, chief global strategist at Nikko Asset Management in Tokyo.
"The impact on global risk assets will probably moderate from here as we are likely past the worst part of the crisis," Vail said in an e-mail. "Neither side wants a war."
U.S. stocks and MSCI's broad gauge of stock performance in 49 countries pared gains just before markets closed after news of two blasts, followed by sirens, were heard in Baghdad late on Wednesday.
MSCI's all-country world index gained 0.10%, while bourses in Paris, Frankfurt and Milan rebounded.
On Wall Street, the Dow Jones Industrial Average rose 161.41 points, or 0.56%, to 28,745.09. The S&P 500 gained 15.87 points, or 0.49%, to 3,253.05 and the Nasdaq Composite added 60.66 points, or 0.67%, to 9,129.24.
The pan-European STOXX 600 index earlier closed up 0.17% and emerging market stocks lost 0.21%.
Spot gold fell 1% to $1,558.60 an ounce, having soared to $1,610.90 earlier in the session, its highest since March 2013.
U.S. gold futures settled 0.9% lower at $1,560.20.
A report showing a surprise build in U.S. stockpiles helped crude prices to fall.
The U.S. Energy Information Administration (EIA) said crude inventories rose by 1.2 million barrels during the week ended Jan. 3. Analysts had expected a decline.
Brent futures fell $2.83 to settle at $65.44 a barrel and U.S. WTI crude settled down $3.09 at $59.61 a barrel. WTI futures earlier hit $65.65, the highest since late April.
U.S. Treasury yields rose after yields on the 10-year U.S. Treasury note overnight dropped to 1.705%, their lowest in more than a month, as worried investors bought U.S. government debt in a safe-haven move after the Iranian attack.
Benchmark 10-year notes last fell 11/32 in price to yield 1.8615%, nearly 20 basis points above the low it hit overnight following the Iranian strike.
In Germany, yields on the 10-year government bond rose to -0.247%, still far below a seven-month high of -0.157% hit on Jan. 2, just before the killing of the Iranian general.
A higher-than-expected U.S. private payrolls number for December also boosted the dollar.
The ADP National Employment Report showed private payrolls jumped by 202,000 jobs after an upwardly revised gain of 124,000 in November. Economists polled by Reuters had forecast private payrolls of 160,000 last month following a previously reported 67,000 rise in November.
The dollar index, tracking the unit against six major peers, rose 0.3%, with the euro down 0.37% to $1.111.
The Japanese yen weakened 0.61% versus the greenback at 109.09 per dollar.
Reporting by Herbert Lash, additional reporting by Kate Duguid in New York; Editing by Bernadette Baum and Nick Zieminski