Senator Ted Cruz on Saturday won in Kansas and battled with Donald Trump for Kentucky in a four-state round of Republican voting, The Associated Press (AP) reported.
Meanwhile, Democrats in three states were choosing between Hillary Clinton and Bernie Sanders.
"God bless Kansas," Cruz declared during a rally in Idaho, which votes in three days. "The scream you hear, the howl that comes from Washington D.C., is utter terror at what we the people are doing together."
The Texas senator was leading Trump by more than a 2-to-1 margin in partial returns in Kansas caucuses, noted AP, and he and Trump were in a tight race in Kentucky caucuses.
Despite the support of many elected officials in Kansas, Florida Sen. Marco Rubio came up short, raising serious questions about his viability in the race. Cruz suggested it was time for other Republican candidates to step aside.
Saturday's GOP races also included Maine and Louisiana, while Democrats voted in Nebraska, Kansas and Louisiana.