European markets gave a weary cheer on Monday as euro zone leaders emerged from-all night talks in Brussels with a deal to keep Greece afloat and part of the euro currency union.

European Council President Donald Tusk announced just as trading started for the week that after months of tortuous negotiations, marathon overnight talks had achieved a third bailout for Greece.

"Euro summit has unanimously reached agreement. All ready to go for ESM programme for Greece with serious reforms and financial support," Tusk tweeted.

"It's a good step to rebuild confidence," added Christine Lagarde, head of the International Monetary Fund.

The pan-European FTSEurofirst 300 index opened up 1.3 per cent to hit a 2-week high while Italian, Spanish and Portuguese bonds rallied in debt markets.

The euro rose initially against the world's other major currencies but dropped back as traders locked in some the profits of recent days. Capital controls imposed by Athens have limited trading in Greek bonds, but Tradeweb data showed two-year yields down 4.81 percentage points.

"It's positive that they've reached an agreement and it should be positive for risk in general," said Vasileios Gkionakis, Global Head of FX Strategy at UniCredit.

"We are seeing a dip in the euro at the moment. But that is because of the moves at the end of last week; generally this should bode well."

Asian stock markets had kept their nerve as Greek talks had dragged on through the European night and as Chinese stocks rose for a third straight session following their recent rout.

Data from China showed exports rose 2.8 per cent in June, while imports slipped 6.1 per cent, in a tentative sign global demand might be on the mend.

The Asian giant reports domestic product data on Wednesday and forecasts are that annual growth slowed to 6.9 percent last quarter.

The CSI300 index of the largest listed companies in Shanghai and Shenzhen added 3 per cent on top of last week's rally of 5.7 per cent. Japan's Nikkei gained 1.6 per cent.

"This is victory in the first battles of a long-lasting war," said Hou Yingmin, analyst at brokerage Aj Securities.

"But it takes time for market sentiment to fully recover from the recent trauma, which was so severe, and bears are likely to make a comeback."

The relief that Greece's future in the euro was now looking more certain damped demand for safe-haven assets. Yields on German government debt rose 3 basis points, dragging those on US Treasuries with them.

Federal Reserve Chair Janet Yellen said on Friday that she expects the central bank to raise US interest rates for the first time in almost a decade this year. She appears before US politicians on Wednesday.

In commodity markets, gold was squeezed back toward $1,150 an ounce as the dollar retained most of its overnight strength.

Oil prices were under pressure meanwhile, as Iran and six world powers looked to be closing in on a historic nuclear deal that would bring sanctions relief for Tehran and thus more crude onto the market.

Brent crude sank $1.24 to $57.49 a barrel and U.S. crude shed 91 cents to $51.83.

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