Updated

Rep. Lisa McClain, R-Mich., called out Nancy Pelosi on Tuesday after the House Speaker referred to her as "that woman," and asked the GOP congresswoman to apologize for her statements regarding Rep. Maxine Waters, D-Calif.

"Speaker Pelosi, you need to learn this woman’s name and that’s Lisa McClain," said the Michigan representative during an appearance on "The Faulkner Focus."

McClain asserted that Pelosi holds her party to a "lower standard" by defending Waters' recent comments in Minneapolis while Republicans such as Marjorie-Taylor Greene and former President Donald Trump faced varying degrees of consequences for their speech.

"The Democrats have set a standard and all I’m asking is Madam Speaker, don’t you think we both should play by the same rules?" McClain asked.

GOP CONGRESSWOMAN FIRES BACK AFTER PELOSI CALLS HER 'THAT WOMAN'

McClain said that despite Pelosi’s comments she will continue to fight to "expose" the double standards exhibited by members of Congress.

The GOP congresswoman also criticized Waters directly, claiming that she found it difficult to "misinterpret" the California representative’s comments urging protesters to become more "confrontational."

 "Words do matter," McClain said.

The back and forth between Pelosi and McClain began after Waters visited an anti-police brutality protest in Brooklyn Center, Minnesota, on Saturday evening, saying demonstrators needed to "stay on the street," demanding justice until meaningful police reform was achieved

McClain appeared to reference Waters during a Monday speech on the House floor.

"Once again, this weekend, we saw a member of the majority openly call for more confrontation in a Minneapolis suburb," McClain said. "That very night, there was a drive-by shooting ... where police and the National Guardsmen were targeted."

McClain added that if roles were reversed and a Republican had told protesters to "get more confrontational," the House majority "would move to strip that representative of their committees and possibly move to expel them Congress."

"That woman on the floor should be apologizing for what she said," Pelosi, told The Hill on Monday.

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McClain responded on Twitter, saying that as "that woman," she wouldn’t "apologize for calling out the double standards" set by Pelosi.

Pelosi said Monday that Waters should not apologize for her comments and called criticism of her words a "misrepresentation by the other side."

Fox News' Audrey Conklin contributed to this report.