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Trump chief of staff Reince Priebus: Trump appealed to people like me

White House chief of staff pick Reince Priebus said Monday that Donald Trump won the election because he attracted Republican voters "like me."

"[Trump] appealed to people, in all respects of our party," Priebus told NBC's "TODAY." "And that takes talent and an ability that Prez-elect Trump has. But it was his message and the delivery that created that incredible night."

Trump named Priebus as White House chief of staff on Sunday, a title considered the highest rank for a White House employee.

Priebus has earned respect from Republicans over his nearly six years as Republican National Committee chairman, proving to be a powerful fundraiser. He will serve alongside Trump campaign chief Steve Bannon, whom Trump named as his chief strategist and senior counselor.

In the "TODAY" interview, Priebus touted Bannon's formal education and time spent in the Navy, calling him "very smart" and "very temperate." He also said he's had a great partnership with the president-elect and learned to get to know Bannon as well as the whole team. Priebus said he expects Trump's son-in-law, Jared Kushner, to be involved as well.

"And it has worked; it's been a great partnership," he said. "[Trump] really wants everyone to understand that he wants to be a president for everyone. No matter your background, your race. He wants to do well for every American across the board."

—Javier E. David and NBC contributed to this report.