* C$ ends at C$0.9949 vs US$, or $1.0051 * U.S. data counters dovish Fed outlook * Bond prices mostly higher By Jon Cook TORONTO, March 27 (Reuters) - The Canadian dollar gave back some gains against the U.S. currency on Tuesday following a strong rally in the previous session and U.S. data eased concerns of more stimulus from the Federal Reserve that had weakened the greenback. The U.S. dollar rebounded on Tuesday from its lowest level in nearly a month after Fed Chairman Ben Bernanke said on Monday the policy of very low interest rates was needed to reduce unemployment, making it clear he was in no rush to reverse course. The greenback was helped by U.S. data that showed home prices were unchanged month-over-month for the first time since July, a sign the battered housing market is stabilizing. Also, a private sector report showed U.S. consumer confidence dipped in March but was nearly in line with forecasts. "We don't have a lot of top-tier numbers for the market to hang its hat on," said Stewart Hall, senior currency strategist at Royal Bank of Canada. "It's such a tight range that it's not really indicative of anything other than watching risk sentiment slide back a bit here." The Canadian dollar ended the North American session at C$0.9949 versus the U.S. dollar, or $1.0051, down from Monday's close at C$0.9912 versus the greenback, or $1.0089. Until the Canadian government releases its 2012-13 fiscal budget on Thursday, Hall said there was little to move the Canadian currency out of its window between parity with the U.S. dollar and C$0.99 against the U.S., or $1.01. Canada's resource-heavy currency also was hurt by a dip in Brent crude oil and as gold eased off its two-week highs on Tuesday. Analysts said the dollar could suffer further in the short term if speculation about the prospect of further mass bond buying, or quantitative easing (QE), persists. However, if U.S. data continues to point to an economic recovery the currency could start to push higher again. "(Bernanke) is flagging the issue that the labor market remains far from being improved and that would be a key issue to doing more QE, which right now is looking quite remote," said Mazen Issa, macro strategist at TD Securities. Europe's debt crisis will also return to the forefront later in the week as investors focus on a weekend meeting of euro-zone finance ministers in Copenhagen and Spain's budget presentation on Friday. Lower risk appetite pushed most Canadian bond prices higher. Canada's two-year bond rose 8 Canadian cents to yield 1.212 percent. The 10-year bond was up 55 Canadian cents to yield 2.126 percent.