* World stocks steady after selloff
* Oil off highs as Iran strike against U.S. seen unlikely
* European stocks rise 0.5%
* MSCI world index 0.5% 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 that 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 United States in a way that would disrupt supplies.
Brent crude futures fell 44 cents to $68.48 a barrel, having been as high as $70.74 on Monday, while U.S. crude dropped 34 cents to $62.93.
European equities meanwhile rose as much as 0.7%, tracking similar gains in Asia. Technology stocks were among the top picks in Europe, mirroring trends in the U.S. overnight.
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 0.1%.
"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 ended 0.24% higher, the S&P 500 0.35% and the Nasdaq 0.56%.
Risk assets continued their rally even as Iran said it was considering 13 scenarios to avenge the killing of General Qassem Soleimani.
Marija Veitmane, a senior strategist at State Street, said she sticks to her expectation of a slight improvement in economic and earnings outlook.
"The world is well stocked with oil and can stomach short disruptions, while large U.S. shale production should soften its impact," said Veitmane, brushing aside worries that an oil price spike would dent global growth.
On Tuesday emerging markets, which had been hit hardest by spiking oil prices, bounced back, with stocks up 0.4%.
That left the MSCI world equity index, which tracks shares in 49 countries, just 0.5% 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 108.38 yen from a low of 107.75 hit on Monday.
Against a basket of currencies, the dollar drifted off to 96.752 but stayed well above a recent six-month trough of 96.355.
The euro and sterling were trading slightly lower ahead of this week's vote in Britain's parliament on Prime Minister Boris Johnson's European Union withdrawal deal.
Bitcoin, the world's biggest cryptocurrency, broke above $8,000 overnight and is up 13% since the U.S. drone attack in Iraq last week. Though it is not seen as a safe-haven asset given its wild swings, the surge has coincided with the equities sell off.
Additional reporting by Wayne Cole; Editing by John Stonestreet and Catherine Evans