Shares in New York have reversed their early gains, which followed US President Barack Obama's announcement that Osama Bin Laden had been killed.
In New York, the Dow Jones closed barely changed on the day.
The benchmark US oil contract earlier fell by more than 2.5% before recovering as investors questioned whether Bin Laden's death would ease political tensions.
Gold prices also initially fell, before rebounding towards another record high.
Silver prices bucked the trend, falling by as much as 11%.
Analysts said that Bin Laden's death could reduce security risks and would help lift consumer sentiment in the US.
But they warned that it would do little to ease the longer-term risks hanging over the US and global economies.
"There is some feel-good value and the market will like that," said Chip Hanlon of Delta Global Advisors.
But he added: "It doesn't change much about the energy situation and doesn't change much about the ongoing battle with radical Islamists."
In Asia, Japan's Nikkei 225 index gained 1.6%, closing above the 10,000 level for the first time since mid-March, when the country was struck by a deadly earthquake and tsunami.
In Europe, London's FTSE 100 was closed for a public holiday, but in Paris the Cac40 closed up 1.9 points at 4,108.8 which in Frankfurt the Dax closed up 13.2 points at 7,527.6.
Several stock markets in Asia, including in China, Hong Kong, Singapore, Malaysia and Thailand, were also closed for a public holiday on Monday.
Oil prices fell in early trading in Europe, but rallied after they opened in New York.
They have been pushed to near record levels in recent weeks by the fighting in Libya, and political instability in the Middle East.
At the same time, producer countries such as Saudi Arabia have increased their output in an effort to ease fears of a supply squeeze.
Analysts said the earlier rise in markets reflected a willingness by investors to put money into riskier assets, in the belief that Bin Laden's death had removed some of the uncertainties hanging over world events.
"There is always a reaction in commodities to news of this nature," said David Lennox of Fat Prophets.
"The markets will always react quickly, and in this case it is someone who has been held out as the father of all terrorism.
But any easing we might see in oil or gold markets, in my view, will be short-lived. The longer-term impact will not be substantial."
But some analysts said Bin Laden's death might actually incite more violence around the world.
"The immediate thing is how it will affect US assets: its embassies, personnel and physical installations," said Arjuna Mahendran, chief strategist at HSBC Private Bank.
"Does it raise the threat level? That's the key thing. I think it does."
The US state department has cautioned its embassies and citizens against the possibility of reprisals from al-Qaeda, the organisation that Bin Laden started and led.
The department has also issued a worldwide travel alert warning of greater potential for anti-American violence.