A federal judge on Friday denied Hunter Biden's request to dismiss a gun case against him that his lawyers argue is politically motivated. 

U.S. District Judge Maryellen Noreika rejected all of Biden motions, which cited vindictive and selective prosecution, thereby moving the case forward to trial. 

The son of President Biden is accused of lying about his drug use on a federal form when he bought a firearm in October 2018, a period when he has acknowledged struggling with addiction to crack cocaine. 

He's pleaded not guilty. 

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Hunter Biden has acknowledged his struggles with substance abuse during that period, but his lawyers have said he didn't break the law and another nonviolent, first-time offender would not have been charged.

His lawyers have argued that prosecutors bowed to political pressure after an immunity provision from an original plea that fell apart was publicly pilloried by Republicans – including former President Trump – as a "sweetheart deal." Prosecutors have denied the case is motivated by politics. 

Noreika has not yet ruled on a challenge to the constitutionality of the gun charges.

The trial is penciled in for jury selection for the week of June 3. 

In California, Biden is still heading toward a trial on June 20 on tax charges. Biden's legal team in that case also plans to appeal a judge's denial of a motion to dismiss the charges. 

"Notice is hereby given that Robert Hunter Biden hereby appeals to the United States Court of Appeals for the Ninth Circuit," the court document giving notice of the interlocutory appeal states. 

Biden is alleged to have participated in a four-year scheme to avoid paying $1.4 million in taxes while living an extravagant lifestyle. The trial in that case is scheduled from late June until mid-July. 

The Associated press contributed to this report.