* World stocks rise, led by Europe
* Dollar slips
* Investors seeking signs of economic improvement
By Jeremy Gaunt, European Investment Correspondent
LONDON, June 9 (Reuters) - World stocks rose on Tuesday, led by a rebound in Europe, while the dollar slipped and investors sought 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.
MSCI's all-country world index was up 0.3 percent, mainly because of gains in Europe.
The FTSEurofirst 300 rose 0.7 percent, recouping 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, pausing from gains versus the euro as investors reassessed whether speculation of a possible rise in U.S. interest rates later this year will push the U.S. currency higher.
The climb in European shares also helped raise demand for riskier trades, boosting the Australian and New Zealand dollars, while hitting the yen.
The U.S. currency was down 0.4 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. Euroe zone government bond yields fell with the 10-year at 3.666 percent and the two-year at 1.705 percent. (Additional reporting by Naomi Tajitsu and Blaise Robinson, editing by Mike Peacock) (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)