Sen. Rand PaulRandal (Rand) Howard PaulOvernight Defense: Senate confirms Haspel as CIA chief | Trump offers Kim 'protections' if he gives up nukes | Dem amendments target Trump military parade Hillicon Valley: Lawmakers target Chinese tech giants | Dems move to save top cyber post | Trump gets a new CIA chief | Ryan delays election security briefing | Twitter CEO meets lawmakers Overnight Finance: Watchdog weighs probe into handling of Cohen bank records | Immigration fight threatens farm bill | House panel rebukes Trump on ZTE | Trump raises doubts about trade deal with China MORE (R-Ky.) said  that he supports more people voting, when asked about the runoff results in Mississippi's GOP primary. 

Sen. Thad CochranWilliam (Thad) Thad CochranMississippi Democrat drops Senate bid Dems look to keep up momentum in upcoming special elections Chamber of Commerce makes play in Mississippi Senate race for Hyde-Smith MORE's (R-Miss.) narrow win Tuesday night by increasing turnout spurred his opponent, state Sen. Chris McDaniel (R), and other conservative critics to allege potential voting irregularities. 

"I'm for more people voting, not less people voting," Paul told reporters on Wednesday, according to The Washington Post

Turnout in the runoff Tuesday increased nearly 15 percent compared to the primary, a reversal from historic trends. 

Cochran fell narrowly short of McDaniel in the primary earlier this month but neither candidate garnered 50 percent, forcing the runoff. Cochran sought to increase his total during the runoff by reaching out to African-Americans and others outside the Republican Party, who would be eligible to vote for him if they did not participate in the Democratic primary. 

On Wednesday, Cochran led by nearly 7,000 votes and McDaniel left open the possibility of challenging the totals in the next few days. 

However, Paul declined to weigh in on the controversy.  Paul, a likely 2016 candidate for president, had earlier this month vowed to stay out of the race. His father, former presidential candidate Rep. Ron Paul (R-Texas), endorsed McDaniel weeks before the runoff, however. 

The Kentucky senator has consistently talked about reaching out to demographics that are traditionally outside the Republican Party in order to expand the GOP brand. He had taken a soft tone on increased voter identification laws, and has announced he will soon introduce a bill that would give back voting rights to some nonviolent felons who completed their sentence.