ROME — Near the beginning of an Italian soccer match in Tuscany on May 23, 2010, a man from Singapore named Tan Seet Eng spoke on the phone with a Croatian associate. He told the associate he needed at least three goals to be scored in the match between Grosseto and Reggina.

“No problem,” the associate said, explaining he had someone working for him at the match.

With that simple exchange, Italian prosecutors say, the fix was in.

The phone conversation illustrated the power of Mr. Tan, a shadowy figure living in Singapore who was called “the boss” and “the capo” by his accomplices and is suspected of fixing dozens of games as easily as he did that 2010 match in Tuscany.

The game is among about 100 matches played from 2008 to 2011 in Italy’s top three soccer leagues that are under investigation — and among 680 matches worldwide considered suspicious by European law enforcement, which reported the results of a 19-month match-fixing investigation last week. European investigators believe Mr. Tan was a common link in many of the matches.