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(CNN) -

Rand Paul is defending his relationship with Mitch McConnell after helping his fellow Kentuckian defeat a tea party-backed challenger in a GOP Senate primary.

"I came out of the tea party movement. I'm very concerned about the debt. I'm very concerned about big government," Paul said on Friday. "But I think the misnomer is to think somehow Senator McConnell isn't. That's what his whole entire career has been predicated upon - fighting against big government."

The comments by Paul, the state's junior senator, came at a news conference with McConnell in Louisville that was focused on building party unity following a bruising campaign in which the minority leader's opponent, Matt Bevin, got 35 percent of the primary vote.

Some in the conservative grassroots movement immediately called for Republican voters to unite and support McConnell.

But Bevin has been noticeably quiet and hasn't said whether he'll back his rival--though he flatly stated on election night that he won't back the Democratic nominee.

That's not stopping Alison Lundergan Grimes, however. She's actively going after Bevin supporters. In an open letter Friday to the 40 percent of Republican voters who didn't vote for McConnell, she argued that a vote for Grimes is a vote for change.

"Yes, we are in different parties, and we have divergent views on some issues. But if you believe that we need a fresh face to shake up Washington, I invite you to join our campaign," the letter stated.

Bevin hit back later Friday with his own letter, saying she doesn't understand "the principles that united my campaign's supporters" and disparaged her stance on a number of items on her agenda.

He agreed with her that Kentucky needs change, but not her kind of change. He made no direct mention of McConnell in the letter.

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Party focused on building unity