Senate Majority Leader Sen. Mitch McConnell (R-KY) wears a mask as he walks through a hallway at the U.S. Capitol May 11, 2020 in Washington, DC.
CNN  — 

Senate Majority Leader Mitch McConnell is continuing to hammer home his message about mask-wearing to fight the Covid-19 pandemic, saying that while he’s not addressing the government’s authority to implement rules requiring masks, everyone should be wearing one.

On Thursday, the Kentucky Republican made clear that he is not getting involved in Kentucky Democratic Gov. Andy Beshear’s battle to mandate facial coverings in public in certain situations.

“I’m not in that fight,” he said at a medical center in Leitchfield, Kentucky. At the same time, he urges Kentuckians to wear masks.

“I know there’s an argument going on here in the state over whether the governor can or cannot make you wear a mask,” he said. “I’m not in that fight. But I’m here to tell you, put it on. The single best way all of us can be responsible to ourselves and sensitive to the health of others is to wear a mask and to practice social distancing.”

The Senate majority leader in recent months has significantly diverged from President Donald Trump, who wore a mask publicly for the first time only over the weekend, rarely urges Americans to wear masks and often boasts about the country’s response while dismissing rising coronavirus cases.

“I’ve been saying over and over and over again, wear your mask,” McConnell said at a press event in Kentucky earlier this week. He added that it’s “the single most important thing” we can do, a sentiment the Republican leader has repeated since early May, often while waving a blue mask in the air.

McConnell wears a mask in public and during Senate sessions, repeatedly saying how important it is to “provide a good example in that regard.”

“It has no idea what a Republican or Democrat is,” McConnell said of the virus Monday at a hospital in Mount Vernon, Kentucky.

It is “astonishing,” McConnell said Thursday, that wearing masks has become a political issue in the middle of a pandemic.

“How this ended up becoming a factor in American politics is a little astonishing to me,” he said. “The coronavirus is not involved in American politics, at all.”

“It’s the right thing to do,” McConnell said, pointing to how Kentucky is “having something of a surge” in coronavirus cases. While Kentucky has so far seen relative success in keeping its case count low, the state is seeing a rise in cases, recently surpassing 20,000, according to Johns Hopkins University data.

“I want to encourage everybody, regardless of who has the authority to require it or not require it, do it,” he said Thursday.

Last week, Kentucky’s governor issued an executive order mandating facial coverings in certain situations, but, it was temporarily blocked by a circuit court on the same day. Beshear continues to fight the court to uphold his mandate.

He is one of several governors across the country who have tried to use their executive power to mandate mask-wearing amid the pandemic, which has led to similar legal clashes in Michigan and North Carolina.

CNN’s Manu Raju, Rebekah Riess and Caroline Kelly contributed to this report.