As United States prosecutors delivered updates on Wednesday in their unfolding corruption case against global soccer officials and business executives, a federal judge expressed eagerness to move the case toward trial.

“Begin to think seriously, given the passage of time, as to when we may proceed to trial,” Judge Raymond J. Dearie of Federal District Court in Brooklyn told the lawyers before him.

The two defendants appearing in court were José Maria Marin, the former head of the Brazilian soccer federation, and Aaron Davidson, an American sports marketing executive.

Both men — two of 41 defendants in the United States case, which centers on members of FIFA, soccer’s world governing body — were charged in May and are under house arrest. The first defendants convicted in the case, all of whom have yet to be sentenced, were charged in 2013.