The oversold euro rose to three-week highs against the dollar on Monday and world stocks edged higher as signs of progress on a Greek debt restructuring deal fuelled hope that the euro zone crisis may be contained.

Oil prices gained as European Union foreign ministers agreed to ban imports of Iranian oil from the start of July to pressure Iran over its nuclear ambitions, a move that renewed threats by Teheran to block a vital oil export route, while investors sold safe-haven U.S. bonds.

In Europe, Germany and France pushed for a deal between Greece and its private creditors and said they remained dedicated to a new bailout needed by March to stave off a disorderly default.

Euro zone finance ministers could decide later on Monday what debt restructuring terms they would accept.

Greece needs additional aid to be able to return its debt to sustainable levels. Without the aid, Athens will not be able to pay back 14.5 billion euros in maturing bonds in March - which would trigger a messy default that would hurt the entire euro zone and send tremors beyond the 13-year-old single currency bloc.

Optimism that Greece will reach a deal with its creditors led investors to pare bets against the euro, even though most maintained a negative outlook.

The euro was up 1.1 percent at $1.3012, after earlier hitting its strongest level since early January.

The euro was supported by investors taking profits on short positions, which have been running at record highs for four weeks, strategists said.

Sentiment continues to outweigh fundamentals, at least for the time being, said Brad Bechtel, managing director at Faros Trading in Stamford Connecticut. This euro short-covering sentiment-driven rally will likely not be sustainable over the medium-term, but may persist over the short-term.

Over the medium-term the euro should remain under pressure with the ECB more accommodative and providing liquidity.

The broad MSCI world equity index <.MIWD00000PUS>, which is up over 5 percent for the year so far, gained 0.4 percent on the day, while U.S. stocks were slightly lower.

Upbeat sentiment over Greece was offset by profit-taking after the S&P 500 registered its best week since Christmas.

The Dow Jones industrial average <.DJI> was up 0.22 points, or 0.00 percent, at 12,720.70. The Standard & Poor's 500 Index <.SPX> was up 1.56 points, or 0.12 percent, at 1,316.94. The Nasdaq Composite Index <.IXIC> was down 2.24 points, or 0.08 percent, at 2,784.46.

The pan-European FTSEurofirst 300 <.FTEU3> index of top shares finished up 0.5 percent, while in Japan, the Nikkei <.N225> ended little changed.

In the oil market, Brent crude futures were up 88 cent at $110.74 a barrel.

The EU also imposed a number of other economic sanctions against Iran, joining the United States in measures aimed at deflecting Tehran's nuclear development program.

The ban of Iranian oil by the EU ministers elicited further threats from Teheran to close the Strait of Hormuz shipping channel. The move could hurt Greece, Italy and other economies that depend on Iranian oil.

The benchmark 10-year U.S. Treasury note was down 12/32, with the yield at 2.0671 percent.

Risk assets bounced, said William O'Donnell, head of U.S. rates strategy at RBS Securities in Stamford, Connecticut. This spasmodic price action may be what we're in for until the Federal Open Market Committee fills in the templates for their rate, growth and inflation projections on Wednesday.

Though also considered a safe-haven asset, gold rose 1 percent a six-week high, boosted by technical buying and as the euro rallied.

(Reporting by Caroline Valetkevitch; additional reporting by Julie Haviv, Robert Gibbons, Frank Tang and Emily Flitter in New York; editing by Dan Grebler)