Donald Trump responded to Hillary Clinton's recent diagnosis of Pneumonia on Monday, Sept. 12, saying he hopes she "gets well" and he plans to release "very, very specific" details about his own health soon. (Jenny Starrs,Bastien Inzaurralde/The Washington Post)

A day after Hillary Clinton fell ill at a 9/11 memorial ceremony in New York, Donald Trump announced on Monday that he underwent a physical last week and will release "very, very specific" results this week.

"Hopefully they're going to be good. I think they're going to be good," Trump said on Fox News on Monday morning. "I feel great."

Trump was standing near Clinton when she quickly left the ceremony Sunday morning. Her campaign later said that she was diagnosed with pneumonia on Friday and grew overheated at the ceremony, but quickly recovered after resting at her daughter's home.

"Like you, I just, I see what I see. The coughing fit was a week ago, so I assume that was pneumonia also. I mean, I would think it would have been, so something's going on," Trump said on Fox News. "But I hope she just gets well and gets back on the trail. And we'll be seeing her at the debate."

Trump was also asked if he thinks the Democratic National Committee will replace Clinton.

"No, I don't think they'll replace her," Trump said. "We have to see what's wrong. I mean, we have to see what's wrong. But whatever it is ... I'm ready. Whatever it is."

Trump also did an interview with CNBC on Monday morning that lasted more than 30 minutes. Joe Kernen, co-host of the CNBC's Squawk Box, pointed out that Trump has been questioning Clinton's stamina for weeks and asked if Clinton's Sunday health incident confirmed his assessment.

"Well, I don't get satisfaction, Joe. And, frankly, you know, I hope she gets well, and I hope she gets well soon," Trump said. "But, you know, it was quite sad, to be honest with you, and I hope she gets well soon. No satisfaction, believe me, whatsoever."

Kernen also claimed that it has been "well documented" that Trump's schedule has been "more grueling" than Clinton's.

"Well, it has been," Trump said. "It's a very tough schedule. You know, you go from one city — we're going to Pennsylvania, Ohio and Florida and, you know, all over over the next, you know, day or so."

Kernen and Trump both seemed to suggest that Clinton's health problems extend beyond pneumonia.

"It was interesting because they say pneumonia on Friday, but she was coughing very, very badly a week ago and even before that, if you remember. This wasn't the first time, so it's very interesting to see what is going on," Trump said. "I want her to get better. I want her to get out there. I look forward to seeing her in the debate. I will say this: The scheduling, you know, if you look at my scheduling and compare it to anybody else's scheduling, there's not a contest. So, you know, I have found the whole challenge to be very invigorating."