* World stocks steady after selloff
* Oil off highs as Iran strike against U.S. seen unlikely
* European stocks rise 0.6%
* MSCI world index 0.4% away from all-time high
By Thyagaraju Adinarayan
LONDON, Jan 7 (Reuters) - World shares steadied and oil pulled back from multi-month highs on Tuesday after dramatic post-new year moves, as investors judged prospects of an all-out conflict between the United States and Iran had eased.
After a strong rally, oil gave back some of its gains amid signs that Iran would be unlikely to strike against the U.S. in a way that would disrupt supplies.
Brent crude futures fell 49 cents to $68.42 a barrel, having been as high as $70.74 on Monday, while U.S. crude dropped 42 cents to $62.85.
European equities meanwhile rose 0.7%, tracking similar gains in Asia. MSCI's broadest index of Asia-Pacific shares outside Japan recouped almost all of Monday's losses.
Stock futures for the S&P 500 firmed 0.2%.
"Geopolitical risk has always felt much worse for markets in the heat of the moment than it does in hindsight, but it's always possible that the next one will bring us into a different era," Deutsche Bank strategist Jim Reid said.
Risky assets started 2020 on the back foot as Tehran and Washington traded threats after a U.S. air strike on Baghdad airport killed a top Iranian commander.
On Monday the mood began to calm, helping U.S. shares recover ground. The Dow rose 0.24%, the S&P 500 0.35% and the Nasdaq 0.56%.
On Tuesday emerging markets, which had been hardest hit, bounced back, with stocks rising 0.4%.
With those gains, the MSCI world equity index , which tracks shares in 49 countries, was 0.4% away from a record high.
"Markets got a lift from the lack of follow-through (after the air strike) as yesterday progressed, and by the end of the session had actually staged a reasonable recovery," Reid added.
Safety plays were out of favour, with gold retreating to $1,569.41 an ounce, after scaling a near seven-year peak overnight. Euro zone government bond yields edged up from around three-week lows.
The calmer mood also saw the yen lose much of its safe-haven gains, with the dollar bouncing to 108.48 yen from a low of 107.75 hit on Monday.
Against a basket of currencies, the dollar drifted off to 97.661 but stayed well above a recent six-month trough of 96.355.
The euro edged up to $1.1192, but faces stiff chart resistance around $1.1240, while sterling made gains to $1.3196 on better UK economic data.
Surveys of service sectors overnight showed an improvement in the United States, UK and EU, suggesting the ISM measure of U.S. services due on Tuesday might also show strength.
"We think the longest U.S. expansion on record still has plenty of legs," said Tom Porcelli, chief U.S. economist at RBC Capital Markets. "To be sure, Iran adds an additional layer of complexity."
"But while the risk of conflict has increased, the reality is this is likely to be limited to proxy skirmishes," he said. "The risk of a "hot" conflict seems low as Iran is unlikely to respond in such a way that risks a significant escalation from the United States."
Additional reporting by Wayne Cole; editing by John Stonestreet