John Kasich

Ohio Gov. John Kasich on the campaign trail last month in Portland, Oregon.

(Steve Dykes, The Associated Press)

CLEVELAND, Ohio -- Ohio Gov. John Kasich broke his silence Monday, making his first public comments since suspending his presidential campaign May 4.

But the Republican still isn't quite sure what to do about Donald Trump.

"I don't know," Kasich told CNN's Anderson Cooper in an interview that aired Monday evening on the cable network. "While I'm not, you know, glued to this, I've read some other stuff that, to me, is too negative. So I'm undecided."

Pressed by Cooper about the "stuff," Kasich added: "I don't think I need to get into specifics, but ... I don't like when he's attacking and putting people down."

Kasich outlasted all other Republicans in a bizarre GOP race that has seen the unconventional Trump tap into deep frustrations with the political system. The governor had trouble raising money and beating Trump anywhere outside Ohio.

Here's what else we learned from Monday's interview:

1. Kasich is upset with Reince Priebus.

After Trump's big win in the Indiana primary, Priebus, the Republican National Committee chairman, declared the New York businessman the presumptive nominee. Kasich saw the move as an endorsement and "completely inappropriate."

With Texas Sen. Ted Cruz dropping out that night, Kasich finally had the one-on-one battle with Trump that he long coveted. "I'm still there," Kasich told Cooper. Priebus "just wanted to get this thing over. I'm not happy about it."

2. Kasich has no interest in an independent bid.

The Washington Post reported over the weekend that some anti-Trump forces in the GOP -- including 2012 presidential nominee Mitt Romney -- are intrigued by the thought of Kasich resurrecting his White House campaign as an independent.

Not happening.

"I'm not gonna do that," Kasich told Cooper. "I gave it my best where I am. I just think running third party doesn't feel right. I think it's not constructive. ... A third party candidacy would be viewed as kind of a silly thing. And I don't think it's appropriate. I just don't think it would be the right thing to do."

3. Kasich (still) has no interest in being Trump's vice president.

"No, I've not changed my mind on that.," Kasich said in response to a question from Cooper. "I've said all along, I have the second best job in America."

What if Trump appealed to Kasich's sense of duty?

"No, I'm not inclined to do that. ... And I'm really actually excited about getting back here with my team for the State of Ohio. And I gave it my best."

4. Kasich clearly is worried about Trump's tone.

"At the end of the day, endorsing is gonna mean a lot," Kasich said. "And frankly, my wife and my daughters have watched this. And if I were to turn around today and endorse him, they'd be like, 'Why, Dad?' And that matters to me. We'll see what he does. He has a chance to move to the positive side and unify this country."

Cooper later asked if Ohio, always a hotly contested battleground in general elections, is a state that favors Trump or Democratic front-runner Hillary Clinton.

"Well, I think that if you're not a unifier you have a big problem," Kasich replied. "If you're gonna double down on negative, it isn't gonna work."

5. Kasich thinks a Clinton win is possible.

"I think it's very, very difficult if you are a divider," he said when asked if Trump could prevail despite his negative tone. "We have to see how Mrs. Clinton performs. She is gonna be the nominee. And we're gonna have to see what she does.

"If she's gonna move far to the left ... then it's an open race. If she ... doesn't have a unifying message, then you know, it's like throw it up. I mean, who wins? But the demographics are a real problem for Republicans if they spend their time bashing Hispanics, turning off African Americans and not getting young people excited.

"I mean, how do you win?"

6. Kasich wants to help other Republicans, if not Trump.

The governor said he recently had a "delightful conversation" with House Speaker Paul Ryan, a fellow Republican who is taking his time warming up to Trump.

"I intend to go out and campaign for House and Senate members," Kasich told Cooper. "I left a message for the head of the Senate campaign committee. If they want me, I will go and help them. Paul Ryan was delighted to hear it."

7. Kasich wonders what could have been.

Continuing that last thought, Kasich added: "One of the things that a friend of mine in New York said is, 'Could you imagine if you were president and Paul Ryan was speaker, you could have changed everything.' Just like we came in in 2010 and '11 and changed Ohio dramatically, I had a partner there. And that's a little bit frustrating. But I told Paul, I said, 'Paul, I'll do whatever you want, whatever you need. If I can appear for people, I'll be for it. ... Whatever makes sense."