President Dmitry Medvedev says he has lost trust in Mayor Yuri Luzhkov. But Luzhkov, targeted in a recent negative media campaign, has said he would refuse to resign in his dispute with the Kremlin.Russian President Dmitry Medvedev fired Moscow Mayor Yuri Luzhkov on Tuesday, three weeks into a corruption scandal that had rocked the country and provided a rare view of a battle for power inside the Kremlin.