With the senior Uruguayan national basketball team, Moglia was the top scorer in points per game, of the 1954 FIBA World Championship, with a scoring average of 18.7 points per game. He was also named to the All-Tournament Team. He won the bronze medal at the 1956 Summer Olympic Games, in Melbourne, Australia. He was also the leading scorer of that tournament, with a scoring average of 26.0 points per game.