"We hope that prosecutors will aggressively pursue any leads on this case," the statement said, while praising prosecutors' decision to appeal the acquittals.
The court on Tuesday acquitted Sreten Popovic and Milos Stojanovic who had been accused of breaching Geneva conventions on the treatment of prisoners of war. The bodies of the brothers were found in a mass grave in Serbia in 2001.
The court "has found that the accusations listed in the indictment were not proved at the trial," judge Vesko Krstajic said in the verdict.
"There is no doubt that the three young men were executed for a completely unknown reason. The three men died with their hands bound and gunshot wounds to their heads," the judge said.
"But the two were not accused of being accomplices in it," Krstajic said.
The US embassy said it expected Serbian authorities "to bring to justice those responsible for the deaths".
The three victims were reportedly visiting their mother when they were arrested by Serbian police in Merdare, a village on the border between Serbia and Kosovo.
They were jailed for 15 days by a magistrate in the Serbian town of Prokuplje for crossing the border without valid travel documents in July 1999, a month after the end of a NATO-led bombing campaign against Serbia over a crackdown against ethnic Albanians in Kosovo.
Following the fall of Slobodan Milosevic's regime in October 2000, several mass graves were found in various parts of Serbia. The remains of the Bytyqi brothers were excavated in Petrovo Selo along with those of 13 other men.
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