* Second fire since last April in landmark district * Tower is part of Kremlin-backed finance centre project MOSCOW, Jan 25 (Reuters) - A fire broke out at a partly-built Moscow skyscraper on Friday, Russian officials said, the second in the Kremlin-backed Moskva City business centre development in less than a year. The blaze erupted before noon on the 24th floor of the Oko ('Eye') tower, but was put out quickly put out, according to a statement on the Emergency Ministry's website.