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An Iowa judge ordered Cristhian Rivera, the 24-year-old illegal immigrant accused of murdering Mollie Tibbetts, held on $5 million cash-only bond Wednesday -- with Rivera's first court appearance coming just minutes after Tibbetts' family members broke their silence about their broken hearts.

Rivera was mostly stoic and looked straight ahead in the courtroom. He wore headphones and used an interpreter when the judge spoke, only answering "Yes" when asked if he understood the proceeding.

Later, given another chance to speak, Rivera declined.

Rivera's lawyer, Allan Richards, filed a motion for a private hearing, after an earlier defense motion for a gag order was rejected. Richards argued the case had already become too politicized.

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Cristhean Rivera, 24, is accused of murdering Mollie Tibbetts.

"The government has weighed in at the highest levels," Rivera's lawyer said.

If convicted of murdering the Iowa University sophomore, Rivera faces life in prison without the possibility of parole.

"Christhian is a young man who has been working a number of years for a respectable business in this community," Richards said before bail was set. "No criminal record. we urge in court to be fair."

A preliminary hearing in the case was set for Aug. 31 at 2 p.m.

Less than a half hour before Rivera walked into court, Tibbetts' family members issued their first statement since Mollie's body was found in an Iowa cornfield.

"Our hearts are broken," the statement said. “On behalf of Mollie’s entire family, we thank all of those from around the world who have sent their thoughts and prayers for our girl."

The statement continued: "We know that many of you will join us as we continue to carry Mollie in our hearts forever. At this time, our family asks that we be allowed the time to process our devastating loss and share our grief in private. Again, thank you for the outpouring of love and support that has been shared in Mollie’s name. We remain forever grateful.”

Fox News' Melissa Chrise and Travis Fedschun contributed to this report.