The euro rebounded from two days of sharp losses on Monday even after an anti-bailout party was victorious in Greek elections, while global stock indexes edged up on confidence in the European Central Bank's new money-printing program.
The electoral results spurred concern over new instability in the euro zone, although the possibility of Greece leaving the bloc was considered remote.
Stocks continued their ECB-driven rally, and energy company share gains helped US stocks to end higher.
The ECB announced a massive bond-buying plan last Thursday meant to buoy the flagging euro zone economy, where inflation has turned negative.
"There was a lot of trepidation in the market going into the Greek election ... but by this morning the Syriza win was priced into the market already," said Robert Francello, head of equity trading for Apex Capital in San Francisco.
MSCI's global share index rose 0.2%, while an index of European shares ended up 0.6%.
On Wall Street, the Dow Jones industrial average rose 6.1 points, or 0.03%, to 17,678.7, the S&P 500 gained 5.27 points, or 0.26%, to 2,057.09 and the Nasdaq Composite added 13.88 points, or 0.29%, to 4,771.76.
A blizzard bearing down on New York emptied Wall Street offices on Monday. But stock exchanges, including the New York Stock Exchange, were expected to be open for normal operating hours on Tuesday.
Energy stocks rose after Abdulla al-Badri, OPEC's secretary-general, told Reuters on Monday that oil prices may have reached a floor and could move higher very soon. The S&P energy index was up 1.4%.
Athens' main index fell, however, and Greek bond yields rose. Ten-year yields rose to more than 9%, while the main stock index fell 3.2%.
Following the outcome of Sunday's vote, the euro hit its lowest against the US dollar since September 2003 at $1.1098 in Asian trading, according to the EBS trading platform.
In late New York trade, the euro was up 0.52% at $1.1262, just off its high for the day of $1.1295.
"Everything that was priced in for euro negative has happened," said John Doyle, director of markets at Washington, D.C.-based Tempus Inc.
Syriza's demands for a debt restructuring have raised the prospect of a stand-off between Athens and other European leaders that might lead to a "Grexit," although financial markets were treating that as a marginal risk on Monday.
Syriza leader Alexis Tsipras promised Greeks on Sunday that the five years of austerity imposed under bailout programs worth 240 billion euros from the European Union and the International Monetary Fund were over.
He later struck a deal with the right-wing, anti-bailout Independent Greeks party to form a government.
In the US Treasuries market, debt prices slipped ahead of $90 billion of fixed-rate supply and a Federal Reserve meeting later this week. Yields on benchmark 10-year notes held steady near 1.82%, around their closing level on Friday.
Oil prices closed lower after an up-and-down session. Brent fell 1.3% to $48.16. US crude lost almost 1%, settling at $45.15, the lowest settlement price for the existing front-month contract.
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