* Euro lifted by German data but retreats from day's high

* Weaker-than-expected U.S. data keeps traders cautious

* SNB says will not tolerate franc strength vs euro

* Dollar, yen dip against high yielders (Updates prices, adds quotes, details)

The euro rose on Tuesday, recovering from multi-week lows against the dollar and yen, after an unexpected gain in German investor sentiment boosted optimism about the euro zone economy.

Sterling also gained as data showed UK consumer prices held steady in July while a rise in the price of oil helped the New Zealand and Australian dollars rebound from Monday's slide.

A modest rise in major stock markets slowed some of the safe-haven demand that lifted the dollar and yen on Monday but risk-taking was limited by unexpectedly weak U.S. housing data that raised concern about the strength of the U.S. recovery.

The euro rose from Monday's two-week low against the dollar after data from Germany's ZEW think tank showed investor sentiment improved more than expected in August to its best level since April 2006. For more see.

But CMC Markets analyst Ashraf Laidi said the lack of follow-through -- euro gains stalled around $1.4155 -- underscored the tentative mood among most investors.

Each recovery in the euro lately is looking more and more short-lived, he said. The question becomes: Is the market betting on a recovery that is far from confirmed?

The euro was up 0.3 percent at $1.4131 EUR, above Monday's two-week low of $1.4045. It hit $1.4155 after the ZEW report. The euro was up 0.7 percent at 133.80 yen EURJPY, while the dollar added 0.2 percent to 94.69 yen.

Sterling rose 1.3 percent to $1.6563 GBP, boosted by better-than-expected inflation data.

The euro pared gains against the Swiss franc to $1.5190 EURCHF= after Swiss National Bank board member Thomas Jordan said authorities won't tolerate franc appreciation against the euro. The SNB has intervened to weaken the franc this year.

Markets welcomed news of improved investor sentiment in Germany, which came shortly after data showed the country, the euro zone's biggest economy, exited recession in the second quarter. But analysts said the hurdles it faces were capping euro gains.

Hans-Guenter Redeker, chief currency strategist at BNP Paribas in London, said tight German credit conditions would continue next year, raising the possibility that the government may have to come up with more measures to help the economy.

Things are not as rosy as suggested by the ZEW, he said.

An unexpected 1 percent slide in U.S. housing starts in July, which followed a 6.5 percent rise the prior month, also unnerved some investors, as did a larger-than-expected 0.9 percent slide in producer prices last month.

The troubling data comes after a survey late last week showed U.S. consumer sentiment fell for a second consecutive month in July, adding to concerns that hopes for a robust rebound in the remainder of 2009 may have been overdone.

We've seen a sharp sell-off in risk in the past two days, with the dollar rising, on worries about the state of the U.S. consumer, said Andy Busch, chief currency strategist at BMO Capital Markets in Chicago. That theme hasn't changed yet despite today's rebound in the euro.