* European shares flat; but Cyprus still a concern * Data latest sign of U.S. housing strength * German government bonds rise, periphery bonds dip By Ryan Vlastelica NEW YORK, March 19 (Reuters) - Global stock markets were mostly steady on Tuesday, rebounding off earlier weakness as investors used the previous two-day decline as an opportunity to pick up beaten down shares. European stocks, along with the euro and oil, had been pressured on concerns over the risk of failure for a bailout deal aimed at saving Cyprus from default and its banks from collapse. While those concerns limited gains in Europe, a strong read on the U.S. housing market was cause for optimism. "Everyone is watching for the possibility of a default, but the housing number was very strong and a reason why I continue to be very bullish," said Wayne Kaufman, chief market analyst at John Thomas Financial in New York. A government spokesman said Cyprus' parliament was likely to reject plans agreed by euro zone officials over the weekend to part-fund a 10 billion euro rescue of the island by seizing between 6.75 percent and 9.9 percent of deposits in Cypriot banks. Euro zone ministers have urged Cyprus to let smaller savers escape the levy, but if parliament cannot agree, it would put the bailout in jeopardy and raise the risk of default. The euro was flat at $1.2954, as were European shares . London's FTSE 100 slipped 0.07 percent and Paris's CAC-40 fell 0.6 percent while Frankfurt's DAX fell 0.3 percent. MSCI's measure of global stock markets was off 0.09 percent. In the United States, the Dow Jones industrial average was up 16.43 points, or 0.11 percent, at 14,468.49. The Standard & Poor's 500 Index was down 0.79 points, or 0.05 percent, at 1,551.31. The Nasdaq Composite Index was down 2.99 points, or 0.09 percent, at 3,234.60. Equities were supported by data showing that groundbreaking for new U.S. homes climbed in February, a sign the nation's housing market recovery was gathering steam. According to the latest Reuters poll of analysts, the S&P 500 is expected soon to hit a record high, though the blistering rise in equities so far in 2013 is unlikely to last. BUND BOUNCE The plan to seize deposits in Cyprus shredded confidence in the 100,000 euro ($129,600) guarantee on savings offered across the European Union and raised fears of bank runs in other debt-strained countries, putting safe-haven German government bonds again in demand. The Bund future built gains steadily through the morning before solid ZEW data tempered some of the demand to leave it up 0.2 percent at 144.25. The benchmark 10-year U.S. Treasury note was up 11/32, the yield at 1.9165 percent. "We are just waiting for another headline out of Cyprus," one trader said, adding that buying Bunds "is the only trade to have on." ECB BACKSTOP While Cyprus's problems are threatening to disrupt the calm brought to the bloc over the last eight months by the European Central Bank's promise to protect troubled countries, that guarantee has also kept the market reaction muted. With stock markets in many parts of the world at or near long-term highs, analysts are taking the drops of the past few sessions in stride. With the exception of German government bonds, the knee-jerk flight to safety seen on Monday was showing signs of subsiding. The cost of insuring the debt of southern euro zone countries against default via credit default swaps was virtually unchanged as midday approached, and the dollar was flat against a basket of major currencies after Monday's rise. In Asian trading, Japanese stocks jumped 2 percent and the recovery in general risk sentiment supported Asian credit markets, narrowing the spread on the iTraxx Asia ex-Japan investment-grade index by five basis points. Oil remained sensitive to the jitters, however, falling 0.6 percent to $108.89. If the situation in the euro zone deteriorates again, analysts warn it could affect the health of the global economy.