LONDON (Reuters) -European stocks held near all-time highs on Tuesday, while euro zone government bond yields followed U.S. Treasuries in climbing higher after U.S. manufacturing data cast doubt on the Federal Reserve's rate cut forecast.

Data on Monday showed U.S. manufacturing grew for the first time in 1-1/2 years in March as production rebounded sharply and new orders increased, highlighting the strength of the economy and raising doubts about whether the Fed could actually deliver the three interest rate cuts outlined in its latest forecast.

By contrast, euro zone manufacturing activity contracted at an even steeper pace in March than in February, as demand continued to fall, data on Tuesday showed.

German inflation eased, data showed. Broader euro zone inflation data is due on Wednesday, and will be closely watched for indications about when the European Central Bank will cut rates.

European stocks rose in early trading, starting the second quarter on a positive note as financial markets re-opened after Easter public holidays. The initial gains eased over the course of the European morning session.

At 1144 GMT, the pan-European STOXX 600 index was flat on the day, having hit a new all-time high earlier in the session. London's FTSE 100 index was up 0.2%, but Germany's DAX slipped 0.1% .

Big European stocks had surged during the first quarter of the year.

Wall Street futures were a touch lower, but still within reach of recent all-time highs. Nasdaq e-minis were down 0.5% and S&P e-minis were down 0.4%.

"That broad upbeat mood which lifted stocks quite impressively across the first quarter seems to be sticking around as we kick off the second quarter," said Fiona Cincotta, senior markets analyst at City Index.

Monday's U.S. manufacturing data sent yields on U.S. Treasuries higher and they rose further on Tuesday, with the benchmark U.S. 10-year yield at 4.3571%, compared to the previous session's two-week high of 4.337%.

The elevated yields lifted the dollar to its highest in almost five months on Monday. On Tuesday the dollar index was steady at 104.94 and the euro was little changed at $1.07455.

Euro zone government bond yields also followed Treasury yields higher. Germany's 10-year yield was up around 10 basis points at 2.394%.

The yen was steady against the dollar at 151.645 . Traders are watching for any signs of intervention from Japanese authorities, after it touched a 34-year low of 151.975 last week.

"The continued run of robust U.S. data is making the lives of Japanese currency officials attempting to support the yen increasingly uncomfortable," said Tony Sycamore, market analyst at IG. He said intervention was unlikely until after the 152.00 level was breached.

Japanese Finance Minister Shunichi Suzuki said on Tuesday that authorities were ready to take appropriate action against excessive currency market volatility.

Oil prices rose, helped by signs that demand from China and the United States could improve, as well as by threats to oil supply.

In the Middle East, an Israeli strike on Iran's embassy in Syria killed seven military advisors, among them three senior commanders, marking an escalation in the war in Gaza between Israel and Hamas, which is supported by Iran. Analysts said Iran's involvement could impact oil supply.

Ukraine struck one of Russia's biggest refineries on Tuesday.

Brent crude futures were up 1.26% at $88.52 a barrel while U.S. West Texas Intermediate crude futures were up 1.42% at $84.91 a barrel.

Spot gold rose 0.4% to $2,259.7 an ounce, having hit a new all-time high. [GOL/]