Republican presidential candidate Ted Cruz talks to reporters before speaking at a campaign event at Generals Sports Bar and Grill in Weare, N.H., on Thursday Feb. 04, 2016. (Photo by Jabin Botsford/The Washington Post)

This post has been updated.

Ben Carson continued to question the ethics of Sen. Ted Cruz's victory in the Iowa caucuses, accusing the Texas Republican of brushing aside actions his campaign took on election night, including leaving voicemails to precinct captains stating Carson was taking a "leave of absence" from the campaign trail.

Cruz's campaign sent an email Monday night that seemed to suggest, incorrectly, that Carson was dropping out of the race after the neurosurgeon told CNN he planned to go home after the caucuses to get a change of clothes rather than go directly to the next voting state. Cruz's campaign also called precinct captains and left messages asking them to tell Carson voters to caucus for Cruz, according to a person who got one.

The voicemails "said that they had heard that Carson was suspending his campaign and to announce that so that the voters could make a decision and maybe encourage them to vote for Cruz," Cruz precinct captain Nancy Bliseman of Denison, Iowa, said in an interview. She didn't get the messages until after the caucus was over and didn't relay the information, she said. She said she got two voicemails -- one a little after 7 p.m., when the caucuses began, and another around 7:30 p.m.

Carson, speaking on Todd Starnes's Fox podcast Friday, compared Cruz's actions to Hillary Clinton's after the Benghazi attacks.

"Not to take corrective action is tacitly saying eh, it’s okay, or as Hillary Clinton said after Benghazi, 'what difference did it make?'" Carson asked. "I’m not saying it levels to the level of Benghazi, I’m saying it’s the same kind of attitude ... it’s water under the bridge, let’s not deal with it."

Carson has called the emails a "dirty trick."

Cruz has been dogged by the issue while campaigning in New Hampshire, asked about it by press and voters.

When asked in Weare, N.H., Wednesday what he would say to skeptical voters wondering if they could trust him, Cruz said the story the campaign sent stating that Carson was going to Florida rather than New Hampshire or South Carolina was accurate.

"The information that was passed on by the political team was true and accurate and it was relevant to the election," he said. Cruz has said he called Carson to apologize.

"The senator has already apologized for not more quickly making that clarification, and there is no evidence that our sharing of this news story impacted Carson’s campaign -- he well outperformed expectations. The voicemails are in line with the reports that were made at that time," Cruz spokeswoman Catherine Frazier said in an email.

"These voicemails do not suggest that he would completely drop out of the race," she wrote.

According to the conservative Breitbart News website, the voicemails state that Carson is "taking a leave of absence from the campaign trail" and that it is important for precinct captains to tell Carson voters that they "not waste a vote on Ben Carson and vote for Ted Cruz." Bliseman said the voicemail posted on Brietbart is the one she got.

Some Cruz surrogates tweeted about Carson Monday night.

Carson campaign chairman Bob Dees said the neurosurgeon was taking a day off and that his campaign has staff on the ground in New Hampshire and a "good grassroots effort" in South Carolina. Dees said that Cruz apologized to Carson.

"The question is whether that apology truly reflected what he felt. If it did, he'd be eliminating some of his mean-spirited campaign tactics and personnel," Dees said. "That’s his decision to make. It perhaps puts an even greater focus on the integrity of Dr. Carson. People like the idea of trusting Dr. Carson with their future. They can't say that when candidates being duplicitous, testing the political wind."

Cruz said Wednesday in Goffstown, N.H., that he doesn't plan to fire any staffers.

"This is not a campaign that scapegoats our staffers, that holds someone out and fires them for political purposes. So, no, we’re not gonna scapegoat anybody," Cruz said.

Speaking on WABC's "Election Central with Rita Cosby," Carson said the materials were not disseminated by "rogue individuals." Carson said if Cruz doesn't agree with what happened he needs to make changes in his campaign; when asked if Carson is surprised Cruz hasn't made changes yet, the neurosurgeon said: “It wouldn’t surprise me if in fact that’s the kind of person he is.”

Businessman Donald Trump  has also hit Cruz for sending out the emails, accusing him of fraud in the caucuses.

Cruz has said that Trump doesn't like losing.

"It is no surprise that Donald is throwing yet another temper tantrum or if you like, another Trumpertantrum," Cruz said Wednesday. 

David Weigel contributed to this story.