Two of the candidates on Donald Trump's list of potential running mates have crossed themselves off -- one of them just a day after hitting the campaign trail with the presumptive Republican nominee.

Sen. Bob Corker, R-Tenn., chairman of the powerful Senate Foreign Relations Committee, withdrew himself from consideration for the No. 2 job. His decision was first reported by The Washington Post.

"I went into it feeling like probably there's a better way for me to serve," he tells U.S. News. "But it was great to be able to sit down and have those conversations, that kind of relationship, and I hope it continues."

Corker, a businessman who was mayor of Chattanooga before he was elected to Congress, gave Trump the news as they traveled aboard Trump's plane Tuesday on a campaign swing to Raleigh, North Carolina.

Describing the conversation as "matter-of-fact," Corker says he was able to have a deeper conversation once he had taken himself out of the running.

Corker tells U.S. News he plans to continue to campaign for Trump, perhaps speaking on foreign policy at the Republican National Convention in Cleveland later this month. And he said the vetting process allowed him to see a side of Trump that the public often can't.

"I think the caricature created around who Trump is is very different than reality," he says. "I think one of the good things that can happen during the campaign is for that to come out and for people to see Trump the person versus sort of how he's been created if you will – not through any maliciousness, but just over time, in the media, that's kind of what happened."

Also Wednesday, Sen. Joni Ernst, R-Iowa, seemed to similarly remove herself from the veep conversation.

Ernst, who traveled to New Jersey on Monday to meet with Trump , told Politico she "made it very clear to him that I'm focused on Iowa."

"I feel that I have a lot more to do in the United States Senate. And Iowa is where my heart is," she said in the interview Wednesday. "I'm just getting started here."

"And I think that President Trump will need some great assistance in the United States Senate and I can provide that," she added. In the meantime, "I will probably participate more as an advocate. I would love to assist him out on the trail."

Unlike Ernst, who said Wednesday she had been given vetting papers by the Trump campaign, Corker had been formally considered, submitting documents to the attorney overseeing the process.

"I'm 63, I pretty well know what I'm good at and what I'm best at doing," Corker says of his decision. "When an opportunity like this comes up, unless you sit down and at least have some discussion about it, then you have some discomfort later in life as to whether you unturned every stone."