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"I never say anything in a fundraiser I wouldn't say at a public event," Rubio (Fla.) told reporters when asked whether the public has a right to know about what candidates say in closed settings. "I mean, it is a public event. And as I said, obviously you can't control what people are going to tell people after you leave."
The New York Times reported Thursday that Cruz voiced doubts about Trump's and Ben Carson's qualifications for the presidency. The comments were notable since Cruz has been careful not to insult Trump in public, as he looks to eventually win over Trump's staunchly conservative supporters.
"Their campaigns have a natural arc. And with both of them I think gravity is pulling them down," Cruz said, according to audio of his remarks released by the Times. Cruz said the terrorist attacks in Paris and San Bernardino, Calif., had given a new level of seriousness to the race.
Cruz said people are now wondering, "who is prepared to be commander-in-chief, who understands the threats we face? Who am I comfortable having their finger on the button? Now that’s a question of strength but it’s also a question of judgment and I think that is a question that is a challenging question for both of them."
The Texas Republican also said he has played nice with both men publicly in the hopes of gaining their supporters.
"My approach, much to the frustration of the media, has been to bear hug both of them and smother them with love ... I believe that gravity will bring both of those campaigns down. I think the lion’s share of both of their supporters come to us."
Cruz's campaign released a statement from him Thursday calling the report "misleading," but not disputing anything specific reported as fact. Speaking at a conservative think tank in Washington Thursday, Cruz declined to comment on his specific remarks.
"But I will say is this: Over the course of the presidential election, the voters are going to make a decision about every candidate, and ultimately the decision is who has the right judgment -- experience and judgment -- to serve as commander in chief. And every one of us running is being assessed by that metric, and that is exactly why we have a democratic election to make that determination," Cruz said.
Rubio and Cruz have voiced disagreement with Trump's call this week to bar Muslims from entering the country over concerns about terrorism. Asked flatly whether he would support Trump if he is the nominee, Rubio gave a roundabout answer.
"I'm going to support the Republican nominee. I believe the Republican nominee's going to be someone that can win the general election. And I don't believe Donald can," Rubio said.
Cruz and Rubio have routinely sparred over national security and immigration in what has become a bitter feud in recent weeks. Rubio once again accused Cruz of being soft on defense Thursday. Meanwhile, Cruz aides took to social media to accuse Rubio of double talk on immigration.
Rubio made his remarks to reporters after giving a speech here calling for reforms to the VA. Later, he traveled north to Ames to address students at Iowa State University.
The veterans-focused event, which included a moderated discussion, was hosted by Concerned Veterans for America, a group backed by the billionaire industrialist Koch brothers' vast political network.
Rubio's older brother Mario Rubio, an Army veteran, was in the audience for the address. It's rare that Rubio campaigns with a family member.
Rubio told the crowd at the event that his brother, 65, has struggled to receive proper dental care under a bureaucratic logjam.
"He was hit in the mouth while in jump school, bending his front teeth back in a way that became an orthodontic nightmare," Rubio said. "He was driven to the dentist at Fort Benning where they did some initial work to correct the damage, but the Army never made an official record of the visit. So today, he needs more orthodontic work as a result of his injury, but the VA won’t cover it."
Rubio has sponsored legislation he says would make it easier to hold executive and lower-level employees at the VA accountable for their performance.
"Those who are not doing a good job will be fired when I am president," said Rubio. As president, the senator noted, he would require the agency to release more information publicly about its overall operations.
Not far from where Rubio was speaking, influential Christian conservative leader Bob Vander Plaats, who heads the group the Family Leader, said Thursday that he is supporting Cruz, adding to the recent momentum Cruz has picked up in Iowa.
Asked before the news broke what his reaction would be if Cruz got that highly sought endorsement, Rubio said: "We're not going to drop out of the race. We're going to continue to work hard."
Katie Zezima contributed to this report.