The first Italian was killed at the scene of the altercation on Monday after the three men began arguing about the past World Cup performances of their respective teams, police said.
"According to our current investigations, the three men got into an argument in the pub in the morning about, among other things, the success of Italy and Germany in previous World Cups," police in Hannover, northern Germany, said.
"After this, the suspect is thought to have left the pub, returned a bit later and fired at the two victims," the statement said.
One 47-year-old Italian died mid-morning of his injuries in hospital. The other, 49, is in a critical condition.
Police are now urgently searching for the suspect, a 42-year-old German man from Hannover. Authorities found a weapon, a 9mm pistol, in the vicinity of the
The two respective teams, Italy and Germany, have had very different experiences in the 2010 World Cup in South Africa.
Italy came into the competition as one of the favourites after winning the 2006 World Cup but crashed out in the group stages after a humiliating loss to Slovakia.
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On the other side, a young German team have stormed to the semi-finals, with a 4-1 win over England and a 4-0 humiliation of a strong Argentina team.
However, historically, Italy has won the World Cup more times than Germany, with four victories (1934, 1938, 1982, 2006) compared to three (1954, 1974,
1990). And Italy ended Germany's World Cup campaign while the country hosted the tournament in 2006 in the semi-finals.