World stocks steadied below a recent 4-1/2 month high on Tuesday while the euro fell as worries about further monetary tightening in China and caution over the euro zone and U.S. economic outlook made investors hesitant.

A pick up in demand for risky assets from last week softened a bit on speculation about a possible rate rise in China this weekend, as well as a Moody's report saying the scale of problem loans at local governments in China may be much bigger than previously thought. [nL3E7I507Y]

In the euro zone, a survey showed growth in the region's dominant service sector slowed for a third straight month in June, and by more than an initial estimate, with sluggish new orders dimming the outlook [nL9E7I4005].

Investors were also waiting to see more evidence the U.S. economic recovery is gaining momentum before taking on more risks especially after world stocks, measured by MSCI, posted their best gain since July 2010 last week.

Part of the reason for the rally last week was better-than-expected data out of the United States. The markets want to see whether that will be continued and whether the soft patch has come to an end, said Jeremy Batstone-Carr, strategist at Charles Stanley.

There is still plenty of reason for most investors to be strategically cautious.

MSCI world equity index <.MIWD00000PUS> was down 0.1 percent after hitting its highest since June 1 on Monday.

European stocks <.FTEU3> and emerging stocks <.MSCIEF> were steady on the day. U.S. stock futures pointed to a slightly weaker open on Wall Street <.SPc1> which reopens later after the Independence Day holiday on Monday.

U.S. crude oil fell 0.2 percent to $94.75 a barrel, in part hurt by the dollar which rose 0.3 percent against a basket of major currencies <.DXY>.

German government bond futures rose 20 ticks.

EURO DOWN, UNDERPINNED BY ECB

The euro fell 0.4 percent after hitting a one-month high near $1.4580 on Monday.

The single currency rose more than 2 percent last week, posting its best weekly performance since January. It suffered a brief setback on Monday after Standard & Poor's warned it would treat a rollover of privately held Greek sovereign debt now being discussed as a selective default.

S&P's warning came after Greece secured a 12 billion euro loan that will prevent it defaulting in mid-July or August. But the focus is on a second assistance package likely to be about the same size as last year's 110 billion euro bailout.

Greek Finance Minister Evangelos Venizelos told Reuters on Monday the country would stave off default not only for its own sake but because its survival is vital for the euro zone and the global economy.

The euro's downside was limited thanks to expectations the European Central Bank (ECB) would raise rates to 1.5 percent on Thursday and signal more tightening.

It's hard to sell the euro aggressively before the ECB meeting, as the ECB is still likely to do more tightening after the July hike, said a Japanese bank trader in Tokyo.

(Additional reporting by Brian Gorman)

China European union