In a statement posted on its Web site, the Alaska GOP said the "only reason" Begich -- the former Anchorage mayor -- won his Senate seat in November is because some voters believed Stevens was corrupt.
Stevens was convicted on seven felony counts, but the U.S. Justice Department said this week it was dropping its case against the Republican amid prosecutorial misconduct.
"We'll look forward to the complete story presenting itself and clearing Senator Stevens' name," said Alaska Republican Party Chairman Randy Ruedrich.
Ohio crash that killed two caught on camera [VIDEO]
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees