Ohio Gov. John Kasich said Ohio voters who cast so many votes for Democrat Danny O'Connor in a solidly Republican district were "sending a message to the Republicans to knock it off."

The Republican governor made the comments in an exclusive interview with CBS News correspondent Ed O'Keefe, following the special election Tuesday night in Ohio's 12th Congressional District that is still too close to call. President Trump and the GOP have declared victory for Republican Troy Balderson, but no major news outlet has yet called the race for either candidate. Kasich suggested he believes a number of Republican women voted for O'Connor over Balderson.

"Well, the voters here sent a message to the Republicans to knock it off," Kasich, who has been critical of Mr. Trump, told O'Keefe. "Stop the chaos, the division, no more of this family separation that we see at the border or taking people's healthcare away. I think that have — basically have had enough and they're sending a message to the Republicans, including the Republican in the White House...And what happened here, in this district, people will not, maybe not understand this. This district is so Republican, there should never even have been an election here. And it was so close and -- in one of the counties that's so solidly Republican -- where a Republican would normally win by 70 percent, it broke basically 50-50."

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"So, some Republicans sat at home, but what I think happened, and we don't have all the numbers yet, I think you will find a lot of Republican women who not only didn't sit at home, but a significant percentage, or some percentage of them voted for the Democrat," he added.

Mr. Trump, who held a rally for Balderson last week, has already taken credit for what he sees as a Balderson win. But Kasich didn't think the president should be so comfortable, and the close race "was a vote on the president."

When I decided to go to Ohio for Troy Balderson, he was down in early voting 64 to 36. That was not good. After my speech on Saturday night, there was a big turn for the better. Now Troy wins a great victory during a very tough time of the year for voting. He will win BIG in Nov. — Donald J. Trump (@realDonaldTrump) August 8, 2018

"Well look, first of all, the seat is overwhelmingly Republican," Kasich said. "It shouldn't have been this close and if this, this really, I don't think, wasn't a vote on Balderson or a vote on the Democrat, I think it was a vote on the president. And I think the message was you gotta stop doing what you're doing. All these tweets, all this disruption, all this chaos, all this division, all the negativity. It has to stop. That's what I think they were saying."

Democrats, Kasich said, are motivated ahead of the midterm elections, and as Republicans battle to hold onto the House, a number of districts are potentially even more vulnerable than Ohio's 12th Congressional District. Republicans, he claimed, are "turned off," and some are beginning to vote for Democrats.

"We may be entering, may on the edge of entering a post-partisan environment where people are gonna start thinking a little more about the person and a little bit less about the party," Kasich said. "In my opinion, that's good for the country, but I hope my party will think about what we're doing in Ohio to help people from top to bottom. To me, that's the winning message."

The former 2016 presidential candidate, who has attempted to keep his profile a national one, also didn't rule out the possibility of another presidential bid Wednesday.

"I've said that all my options are on the table," Kasich said. "I happen to believe -- and I'm a positive populist, the president is a negative populist -- I believe that people do have serious problems, but I think they can be lifted. I don't play the victim game. Now, I don't know where that's gonna take me, but I'm gonna keep doing what I have been doing for several years now -- and including on that debate stage -- to talk positively about the future of our country."