With the senior men's Italian national basketball team, Fučka played at the 2000 Summer Olympic Games, and he won the gold medal at the FIBA EuroBasket 1999, where he was named the tournament's MVP. Fučka also won a silver medal at the FIBA EuroBasket 1997. He also played at the 1998 FIBA World Championship (selected to the All-Tournament Team), and at the FIBA EuroBasket 1995 and the FIBA EuroBasket 2001.