World equity prices rallied on Monday as investors welcomed a conditional agreement to negotiations aimed at keeping Greece afloat with a bailout and to stay within the euro zone.

European equities surged almost 2 per cent while Wall Street jumped more than 1 per cent after euro zone leaders made Greece surrender much of its sovereignty to outside supervision in return for agreeing to talks on an 86-billion-euro bailout.

However, investors were anxious that a deal was not entirely in hand and that international lenders, led by Germany, obliged leftist Prime Minister Alexis Tsipras of Greece to abandon his promises of ending austerity.

The deal is contingent on Greece meeting a tight timetable to enact reforms of value added tax, pensions and budget cuts.

"This is not over yet. In fact it might be far from over," said Anthony Lawler, a portfolio manager who invests in hedge funds at investment firm GAM in London. "It is not at all certain that the Greek government will accept what is proposed."

The conditional deal turned the focus in foreign exchange to a potential rate hike by the Federal Reserve in September. Comments from central bank Chair Janet Yellen and Boston Fed President Eric Rosengren on Friday suggested that could be likely.

"Barring new weakness in economic data, the Fed will raise rates in September," said Marc Chandler, global head of currency strategy at Brown Brothers Harriman in New York.

The euro fell more than 1 per cent as the Greek deal renewed focus on the prospect that the US Federal Reserve might hike interest rates in September. The euro fell 1.45 per cent to $1.1000, at times weakening to below that psychologically important level. The dollar gained 0.53 per cent to 123.39 yen.

The euro zone's blue-chip Euro STOXX 50 index hit a two-week high, closing up 1.8 per cent, while the pan-European FTSEurofirst 300 index gained 1.9 per cent to close at 1,572.05.

MSCI's all-country world stock index rose 0.89 per cent.

"We're seeing a relief rally," said Andrew Milligan, global head of strategy at Standard Life Investments in Edinburgh. "As we go through the details, however, it's very clear that there is a sizeable number of hurdles to jump over, especially in Athens."

On Wall Street, the Dow Jones industrial average closed up 217.27 points, or 1.22 per cent, to 17,977.68. The S&P 500 rose 22.98 points, or 1.11 per cent, to 2,099.6 and the Nasdaq Composite gained 73.82 points, or 1.48 per cent, to 5,071.51.

The technology index led the US market higher, with Facebook, Netflix and Amazon all hitting record closing highs.

US Treasury yields rose, but soon pared much of their gains, while yields on low-rated government debt in Europe closed the gap on safe-haven German alternatives.

Benchmark US Treasury 10-year notes were last down 6/32 in price to yield 2.4373 per cent.

The gap between Italian and German bond yields narrowed to a two-month low of 1.14 per centage points in early trading, but later widened to the 1.23 per cent level seen three weeks ago.

Oil prices came off their lows after an Iranian official indicated the Islamic Republic might miss another deadline in securing a nuclear deal integral to lifting Western sanctions on its crude exports.

Crude futures had fallen nearly $2 a barrel on reports that Iran and world powers were closing in on a deal that would allow Iranian oil to re-enter an over-supplied market.

Brent crude for August fell 88 cents to settle at $57.85 a barrel. US light crude, also known as West Texas Intermediate (WTI), settled down 54 cents at $52.20 a barrel. – Reuters