May 13 (Reuters) - The euro fell to its lowest in a month against the dollar on Tuesday, while Bund futures rose along with stocks with traders citing a media report that the Bundesbank would back a rate cut, if needed, by the European Central Bank. The Dow Jones report, which quoted an unnamed source, said that the Bundesbank was also willing to back a negative rate on bank deposits and purchases of packaged bank loans if needed to keep inflation from staying too low. The euro fell past support at its 100-day moving average of $1.3740 to $1.3715, down 0.3 percent on the day and its lowest since April 7. German Bund futures rose to a day's high of 145.08 after the comments, to trade 31 ticks up on the day. The FTSEurofirst 300 index of top European shares slightly extended its gains, up 0.2 percent at 1,367.09 points.

Source