"The likelihood of Hitler being able to accomplish his goals would have been greatly diminished if the people had been armed," he told CNN on Thursday.
An anti-Semitism monitoring group says linking US gun control to the Holocaust is "historically inaccurate".
Mr Carson is polling second in the Republican race behind Donald Trump.
On Friday, Mr Carson reiterated his views about gun control.
"Basically, what I said is when tyranny occurs traditionally around the world, they try to disarm the people first," Mr Carson told the National Press Club in Washington.
The retired neurosurgeon drew condemnation last month for saying a Muslim should not run for president because Islam was inconsistent with the US constitution.
On Friday, he compared his view to the constitutional requirement that a president be a natural-born citizen.
America's founders, he said, didn't "even want to take the slightest chance to put someone in that position who had divided loyalties".
After a week of uttering one controversial remark after another, many of which made US headlines, Ben Carson gave a lunchtime address in the proverbial lion's den - the National Press Club in Washington.
Early in his speech, he acknowledged what everybody in the audience already knew.
"I'm not politically correct," he said. "And that's one of the reason why some of the people in the press don't like me. But it's OK. What I really love is this country. I don't really care if the press likes me or not."
As his speech concluded, Mr Carson left little doubt about what he thought of criticism in the media of comments he said were taken out of context, noting that the American people "were on to" a biased press corps.
"We're doing well," said the man who is second only to Donald Trump in national polls. "And the more they attack me, the better I do."
During the CNN interview, Mr Carson was asked about part of his new book, A More Perfect Union, where he wrote "through a combination of removing guns and disseminating propaganda, the Nazis were able to carry out their evil intentions with relatively little resistance".
He was then asked by CNN presenter Wolf Blitzer: "Just clarify, if there had been no gun control laws in Europe at that time, would six million Jews have been slaughtered?"
Mr Carson said he doubted Hitler would have been able to achieve his goals if Germans had been armed at that time.
"I'm telling you that there is a reason that these dictatorial people take the guns first," he added.
The Anti-Defamation League, an anti-Semitism monitoring group, has previously said that drawing comparisons between the gun control debate in the US and the Holocaust was "historically inaccurate and offensive", especially to Holocaust survivors and their families.
In 1943, armed Jews in the Warsaw ghetto fought the Nazis. Jews killed about 20 Nazis, but about 13,000 Jews died in the uprising.
Ben Carson's comments come days after a mass shooting at a college in the US state of Oregon, in which nine people were killed.
Speaking after the attack, Mr Carson said: "I would not just stand there and let him shoot me. I would say, hey, guys, everybody attack him. He may shoot me, but he can't get us all."
Survivors and relatives of gun attacks in the US have described his comments as insensitive.

Becky, 16, was reported missing on 19 February. Body parts were found at a house in the Barton Hill area of Bristol on 2 March.
Nathan Matthews, 28, from Warmley, appeared by video link at Bristol Crown Court charged with her murder.
Mr Matthews, who has yet to enter a plea to the allegation, was told a provisional trial date had been set for October.
His girlfriend, Shauna Hoare, 21, who is charged with perverting the course of justice, also appeared by video link.
Four other defendants have been charged with assisting an offender.
Jaydene Parsons, 23, appeared via video link, while James Ireland, also 23, appeared in person.
Karl and Donovan Demetrius, both 29, did not appear.
US Republican presidential hopeful Ben Carson has defended comments that suggested the Holocaust may have been avoided if people had been armed.
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The stepbrother of teenager Becky Watts is set to stand trial for her murder.