Republican presidential candidate Ben Carson is fighting back against the backlash he has received for remarks he made regarding Muslims in politics, asserting he will not "back down" from sharing his beliefs.

Carson, the former neurosurgeon gaining ground on frontrunner Donald Trump in recent weeks, first sparked controversy during a Sunday appearance on "Meet the Press." During the segment, NBC's Chuck Todd asked Carson, "Do you believe that Islam is consistent with the Constitution?"

"No, I do not," the typically soft-spoken GOP hopeful responded. "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that."

Carson was widely criticized for his comments, with one Muslim civil rights organization even calling on him to suspend his campaign. However, in an email sent to supporters on Wednesday, Carson staunchly defended his stance: "If you've been following the latest 'controversy' over my comments about Islam, you know the arrows are out for me," he wrote.

"These are my beliefs and I will not back down," he continued in the email. "Many parts of Sharia Law are not compatible with the U.S. Constitution. Under Sharia, homosexuals -- men and women alike -- must be killed. Women must be subservient. And people following other religions must be killed as well."

He acknowledged that while there are "many peaceful Muslims who do not adhere to these beliefs," he cannot advocate any Muslim candidate for president "until these tenets are fully renounced."

Carson went on to ask for help to push back: "Please stand in support of our shared values and help me show the power of "We the People" by making a donation now," his message concludes.

Such tactics have proven effective; Carson told Fox News on Wednesday that the donations have poured in following his remarks: "The money has been coming in so fast, it's hard to even keep up with it," he said. "I remember the day of the last debate, within 24 hours we raised $1 million. And it's coming in at least at that rate if not quite a bit faster."

He also charged that "political correctness" bears the responsibility for the criticism he has faced.

"I've come to be familiarized with the PC culture and I'm willing to fight it. You know, somebody has to stand up for who we are," he said. "We need to be proud of who we are...I want to support what made us great, and what made us unique.

Carson is polling in third place, according to the latest CNN/ORC poll out this weekend, with controversial businessman Donald Trump in the lead, followed by former Hewlett-Packard CEO Carly Fiorina.