Pataki, the former Republican governor of New York, sent a letter to the more than a dozen other GOP candidates asking them to join him in calling out Trump for calling illegal immigrants
to the U.S. "rapists" and "killers."
Trump has not backed down from his comments despite businesses and media organizations severing their relationships with the Trump brand.
"The last week of news coverage over the language used by Donald Trump to describe Mexicans has left me and a lot of other sensible people wondering what century we are living in," Pataki said in his open letter.
He compared Trump's rhetoric to the language used about Italian and Irish immigrants a century ago.
"Here we are in 2015 and a leading candidate for the GOP nomination for president is calling Mexicans criminals, rapists and drug dealers. This is unacceptable," said Pataki, one of the most moderate Republicans running for the White House.
Trump captured 12% of Republicans' support in a CNN/ORC poll released on Wednesday
, coming in second only to former Florida Gov. Jeb Bush
. Pataki, meanwhile, earned less than 1% of the vote in the survey.
Reaction to Trump from other Republicans has varied -- some tried to laugh him off, others said they didn't need Pataki's letter to denounce the businessman's remarks.
South Carolina Sen. Lindsay Graham
, who also is in the back of the pack, according to polls, has long been a supporter of bipartisan immigration reform despite opposition from conservatives.
Speaking in Fort Dodge, Iowa, on Wednesday, Graham said he didn't "need a letter from Gov. Pataki" to repudiate Trump's comments.
"I said from day one that when you label a group of people as rapists and and drug dealers, that's more about you than it is them," Graham said. "I've been trying to fix illegal immigration in a sound, thoughtful way for a decade, so what Trump says says more about Trump than it does anybody else."
Other Republicans on Wednesday who received the letter declined to directly heed Pataki's call.
"I like Donald Trump. I think he's terrific, I think he's brash, I think he speaks the truth," Texas Sen. Ted Cruz
said Tuesday morning on Fox News. "And I think NBC is engaging in political correctness that is silly and that is wrong."
Many of the other competitors have derided Trump's antics, some even before Pataki's letter.
At a press conference last week, New Jersey Gov. Chris Christie
called Trump's remarks "wholly inappropriate."
And Bush said Saturday that Trump's comments were "wrong."
Sen. Rand Paul
brushed off questions about Trump's comments on Monday.
"I really haven't watched Donald Trump too much," the Kentucky senator told CNN, chuckling. "I don't know what he's been saying, but uh, he apparently is drawing a lot of attention."
The campaign for Florida Sen. Marco Rubio
, a Cuban-American who once fought for bipartisan immigration reform, did not respond to a CNN request for comment.
Pataki said his party needs to do more than talk the talk when it comes to paying lip-service to Latino voters, the fastest growing voting bloc, if it wants to wrest control of the White House away from Democrats.
"My fellow Republicans like to talk about how we have to appeal to the Latino vote if we are going to win back the White House. They speak some Spanish, boast about "telling it like it is," or counsel to not be afraid to lose the primary to win the general -- yet so far have been silent when it comes to denouncing these sad and divisive remarks," Pataki said. "As Donald Trump doubles down, I'm asking you to join me in standing up."
Trump responded to Pataki via Twitter on Wednesday, saying ".@GovernorPataki was a terrible governor of NY, one of the worst -- would've been swamped if he ran again!"