* World stocks rise slightly, led by Europe
* Dollar slips. Wall Street set for negative open
* Investors seeking signs of economic improvement
By Jeremy Gaunt, European Investment Correspondent
LONDON, June 9 (Reuters) - World stocks steadied on Tuesday, with Europe providing most gains, while the dollar recovered losses after a bigger-than-expected fall in German industrial output.
Wall Street looked set for modest losses at the open. Investors were seeking fresh signs that the global economy is at least not getting worse.
Some evidence was available from Britain, where house prices in England and Wales fell at their slowest annual pace for 1-1/2 years, and Japan, where two key indicators prompted the Cabinet Office to say its country's economy was bottoming.
Australian business confidence also jumped in May, by the most since 2001.
But ranged against that was industrial output in Germany, Europe's largest economy, falling 1.9 percent month-on-month in April.
"This shows how battered the economy looks," said Thomas Amend, an economist at HSBC Trinkaus. MSCI's all-country world index was up 0.1 percent, off its highs, mainly because of gains in Europe.
The FTSEurofirst 300 rose 0.4 percent, recouping some of Monday's losses. Japan's Nikkei fell 0.8 percent.
"The market is now heading into a consolidation phase," said Jacques Henry, analyst at Louis Capital Markets, in Paris.
Falling equity valuations and mixed signals on the world economy are making investors reluctant to push further in the sharp rally that began in early March. But there is little evidence of a large retrenchment setting in.
Investors are essentially waiting to see whether a true economic rebound is in the offing after various signs that decline has eased.
"On balance, our view is that the global economy is still in the midst of a severe and dangerous recession, but, importantly, the massive policy initiatives around the world have begun to bear some fruit," Bob Doll, chief investment officer for global equities at BlackRock, said in a note.
WEAKER DOLLAR
The dollar slipped as investors questioned whether there was a strong enough chance of a U.S. interest rate rise later this year to justify pushing the currency higher.
The euro fell after the German industry figures.
The U.S. currency was down 0.3 percent against a basket of currencies.
"The market has not moved significantly towards dollar-positive sentiment, and it's fair to expect that investors are unwilling to take on strong positions (in favour of the U.S. currency)," said Michael Klawitter, senior currency strategist at Dresdner Kleinwort in Frankfurt. Euro zone government bond yields fell with the 10-year at 3.673 percent and the two-year at 1.752 percent. (Additional reporting by Naomi Tajitsu and Blaise Robinson) (To read Reuters Global Investing Blog click on http://blogs.reuters.com/globalinvesting; for the MacroScope Blog click on http://blogs.reuters.com/macroscope; for Hedge Fund Hub click on http://blogs.reuters.com/hedgehub)