Washington (CNN) House Freedom Caucus Chairman Mark Meadows issued a blunt warning to House Speaker Paul Ryan on Wednesday, suggesting if he fails to address conservatives' concerns on immigration he'll risk his top leadership post.

"I can say it is the defining moment for this speaker. If he gets it wrong it will have consequences for him, but it will also have consequences for the rest of the Republican Party," Meadows said at an event with fellow House conservatives on Capitol Hill on Wednesday.

The North Carolina Republican stressed, "this president was elected largely on an immigration issue that defined him differently than the other candidates and so it is the defining moment, more so than the budget or anything else that we've passed."

Ryan's office did not provide a response to Meadow's comments.

Ohio GOP Rep. Jim Jordan also piled on Ryan, a Wisconsin Republican. He criticized Ryan for backing the budget deal that avoided a government shutdown last week, tweaking the speaker, who rose to national prominence for his focus on cutting deficits.

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