* Safety rush turns to relief rally as Mideast tension eases
* Europe and Australia return to record highs, Nikkei adds 2.3%
* Yen slides to two-week low
* First two-day fall for gold since November
* Support for oil hints at caution remaining
* World FX rates in 2020 tmsnrt.rs/2egbfVh
By Marc Jones
LONDON, Jan 9 (Reuters) - World markets looked to have overcome their new year wobbles on Thursday, as the United States and Iran backed away from conflict in the Middle East.
U.S. President Donald Trump's suggestion that Iran was "standing down" after it fired missiles at U.S. forces in Iraq had helped give Asia its best day in weeks and saw Europe's STOXX index reclaim its all-time high record.
Wall Street futures were also pointing upwards as more confident traders edged out of the yen, gold and government bonds where they had taken shelter.
Iran fired missiles at military bases housing U.S. troops in Iraq on Wednesday in retaliation for a U.S. drone strike that killed a top Iranian general. But in an address on Wednesday, Trump said no Americans were hurt and made no direct threats of a military response, although he did say there would be more, albeit unspecified, economic sanctions.
Iranian Foreign Minister Mohammad Javad Zarif had earlier said the strikes "concluded" Tehran's response to the killing of its general, Qassem Soleimani.
"The obvious first conclusion to make is that we see the potential for further yen depreciation going forward," said MUFG's EMEA head of research, Derek Halpenny, adding that the likelihood of a major conflict was now low.
The yen, considered a safe haven during geopolitical turmoil because of its deep liquidity and Japan's current account surplus, continued to reverse its 2020 gains in European trading. It was last down 0.3% at 109.4 to the dollar, its lowest in a week and a half.
Another safe currency, the Swiss franc, also fell against both the dollar and the euro..
In Asia, stock markets had taken their cue from Wall Street's overnight bounce. MSCI's broadest index of Asia-Pacific shares outside Japan rose 1.3%, its biggest gain in almost a month.
Hong Kong's Hang Seng Index and Shanghai blue chips each added more than 1.2%. Japanese stocks gained 2.3% to their highest for the year.
Australian stocks rose 0.8% to a record closing high. Futures markets pointed to gains continuing in the United States, with S&P 500 futures up 0.3% and Dow futures 0.4% higher.
"I think today is a bit of a relief rally," said Shane Oliver, Chief Economist at AMP Capital in Sydney. "Yesterday, investors were fearing the worst... The news overnight has been more along the lines that Iran pulled its punches and Trump is toning things down."
Iran's missile attack on U.S. army bases in Iraq on Wednesday had sent gold blasting above $1,600 an ounce and boosted the yen by almost 1% and oil by $3 a barrel.
But it took just hours for that safe-haven dash to fade and for world equities to resume their climb.
Oil is now cheaper than it was before Friday's killing of Iranian commander Soleimani. Brent futures steadied at $65.40 per barrel, about where they began the year.
Gold fell to $1,545 per ounce, giving back Wednesday's gains but remaining more expensive than it was before Soleimani's death, suggesting investors' fears have not evaporated completely.
U.S. Treasuries, which had soared in the flight to safety, also settled back though. Yields on the benchmark 10-year U.S. Treasury note were at 1.8685%, after dropping as low as 1.705%.
Europe's benchmark yields were at one-week highs too, with the benchmark German Bund yield almost 4 basis points higher at -0.22% which was not far off seven-month highs.
Brexit-bound sterling took a dip to $1.3028, its lowest level since Dec. 27, as Bank of England Governor Mark Carney said it could provide a "relatively prompt response" if the UK economy looked like it was facing prolonged weakness.
The better risk appetite though was also evident in emerging markets. China's trade-exposed yuan reached a five-month high of 6.9281 per dollar and South Africa's rand and Turkey's lira that had both been buffeted this week, saw rebounds.
"All is well - so says Trump! That is the mood today," said Bank of Singapore currency strategist Moh Siong Sim.
Additional reporting by Tom Westbrook in Singapore, editing by Larry King and Nick Macfie