Ryan endorsed Trump last week, immediately before the businessman sharpened his attacks on Curiel, accusing the Indiana-born judge of ruling unfairly in a civil case against Trump concerning Trump University because he is "Mexican," and Trump is proposing tough immigration policies along the US-Mexico border.
"I'm building a wall," Trump told the Wall Street Journal last week. "It's an inherent conflict of interest."
Ryan insisted that his support for Trump is rooted in his agenda project, arguing that there is a better chance that the business mogul would sign these policies into law than Clinton would if she were to become president.
"I do absolutely disavow those comments. I think they're wrong. I don't think they're right-headed. And the thinking behind it is something that I don't personally relate to," Ryan said. "But at the end of the day, this is about ideas, this is about moving our agenda forward, and that's why we're moving the way we're moving."
Ryan acknowledged that Trump's comments have undercut his quest to put forth his policy agenda: "I'm not even going to pretend to defend them, I'm going to defend our ideas."
Pressed by a reporter on how he can support Trump in spite of his "textbook" racist comments, Ryan said, "I don't know what's in his heart but I think that comment itself is defined that way".
Republican Senator John McCain was also critical of Trump.
He tweeted: "Judge Curiel is what the American Dream is all about - we should celebrate the fact that our nation produces people like him, not attack them."
Indiana Republican Senator Dan Coats also took to twitter to admonish Trump:
"Donald Trump's comments about the ethnicity of Judge Curiel, who was born in Indiana, were totally inappropriate."
I don't know what's in his heart but I think that comment itself is defined that way
But New Jersey Governor Chris Christie, who is running Trump's transition project, broke sharply with Republicans critical of the business mogul's remarks and defended Trump over allegations of racism.
"Donald Trump is not racist," Christie told reporters outside his polling place in New Jersey. "The allegations that he is are absolutely contrary to any experience I've had with him over the last 14 years."
Christie said Ryan "is entitled to his opinion," but argued that Trump's comments against a federal judge of Mexican heritage did not show him to be racist. Asked whether he thinks Trump has made comments he should not have made, Christie said he had and attributed it to Trump's candor.
"That happens to anybody in politics who speaks their mind," Christie said. "If you have this many cameras and microphones in front of you. . . and if you're not a pre-programmed, robotic politician, you're going to make statements you wish you could take back."
Referring specifically to Judge Curiel, Christie said, "I don't know this judge, I don't know him personally, I don't know the history of the Trump University case, so I'm not going to get into speaking about that."
Christie, who said he cast his ballot for Trump, said "what matters here is winning and losing, first and foremost," and that Republicans must support Trump to defeat presumptive Democratic nominee Hillary Clinton.
"In a field of 17 people, Donald won, and every part of me wishes it was me today, but it's not," Christie said.