* Asian stock markets : tmsnrt.rs/2zpUAr4
* Nikkei up 1.3%, futures point to firm European start
* Oil retreats on doubts Iran would disrupt supplies
* Safe-havens pull back, with yen and gold easing
By Wayne Cole
SYDNEY, Jan 7 (Reuters) - Asian shares rebounded on Tuesday as investors' reassessed the risk of an all-out conflict between the United States and Iran, while Wall Street battled back to the black as tech stocks climbed.
Oil surrendered hefty gains as some speculated Iran would be unlikely to strike against the U.S. in a way that would disrupt supplies, and its own crude exports.
"Oil traders have been unwinding their hedges, thinking that Iran's economic hardships would deter an attack on any oil infrastructure in that it would likely freeze out any existing Iranian exports and put the economy into an even deeper hole," said Stephen Innes, chief Asia market strategist at AxiTrader.
Brent crude futures fell 86 cents to $68.05 a barrel, having been as high as $70.74 on Monday, while U.S. crude dropped 77 cents to $62.50.
Gold also retreated to $1,558.67 an ounce, after scaling a near seven-year peak of $1,582.59 overnight.
Equities went the other way as MSCI's broadest index of Asia-Pacific shares outside Japan added 0.7%, recouping almost all of Monday's losses.
Japan's Nikkei rallied 1.4% and Shanghai blue chips 0.5%. E-Minis for the S&P 500 firmed 0.2%, while EUROSTOXX 50 futures rose 0.4% and FTSE futures 0.6%.
Asian shares fell sharply on Monday as Iran and the United States traded threats after an U.S. air strike on Jan. 3 killed a top Iranian commander.
The mood calmed a little as the session passed with no new aggression.
Instead there was much confusion when the U.S. military wrote to Iraq on Monday saying it would pull out of the country, a letter seen by Reuters showed.
Yet U.S. Defense Secretary Mark Esper told Pentagon reporters that no decision had been made and the military said the letter was only a poorly worded draft.
Wall Street chose to hope for the best and the Dow rose 0.24%, while the S&P 500 gained 0.35% and the Nasdaq 0.56%.
Surveys of service sectors out overnight showed an improvement in the United States, UK and EU, stirring speculation the closely-watched ISM measure of U.S. services due later Tuesday will 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 argued. "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."
The calmer mood 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.
The euro edged up to $1.1192, but faces stiff chart resistance around $1.1240, while sterling made gains to $1.3173 on better economic data at home.
Against a basket of currencies, the dollar had drifted off to 97.661 but stayed above the recent six-month trough of 96.355.
Editing by Shri Navaratnam and Christian Schmollinger