BERN, Switzerland — As Swiss authorities again carried out the wishes of United States law enforcement early Thursday, arresting two global soccer officials in Zurich who had been indicted in Brooklyn federal court, American prosecutors praised Switzerland as a critical partner in the Justice Department’s corruption case.

But in contrast to that publicly harmonious partnership, government officials from the two countries have hardly worked in lock step. Swiss authorities have been wary of appearing as puppets of the United States, according to people familiar with the thinking of Switzerland’s Office of the Attorney General, and they are eager to telegraph that the United States is not Switzerland’s most vigilant policeman.

Several United States government agencies — notably the United States attorney’s office for the Eastern District of New York, the New York field office of the F.B.I. and the I.R.S.’s criminal investigation unit — have spent years investigating what they call a global network of soccer officials and businessmen who have participated in corruption schemes amounting to hundreds of millions of dollars. They have needed cooperation from many countries, especially Switzerland because it is home to FIFA, soccer’s world governing body, based in Zurich.

But Switzerland’s privacy laws have stoked a behind-the-scenes competition, keeping potential key evidence out of the immediate reach of American prosecutors at the same time that Swiss prosecutors have trumpeted their own independent criminal inquiry into global soccer’s top leadership.