"It is a great country and you've just made it a lot greater," Kaine told Clinton, the Virginia senator recounted Friday morning on CNN's "New Day."
Kaine told CNN's Alisyn Camerota that joining Clinton onstage Thursday night after she accepted the Democratic nomination was "a very, very emotional moment" and called Clinton's speech "such a contrast" to Republican nominee Donald Trump's speech at the Republican convention.
"It was kind of midnight in America," Kaine said of Trump's speech. "Her speech was morning in America."
Kaine also slipped into the vice presidential nominee role of attack dog Friday morning as he slammed Trump's recent comments calling on Russia to dig up and release thousands of Clinton's emails.
Kaine called the comments "temperamentally a disqualification for the office" and rejected Trump's defense that they were "sarcastic."
"I don't have a sense of humor about cyberterrorism," Kaine said. "I don't think he was being sarcastic, I think he was being ignorant."
In a later interview with CNN's Jake Tapper, to air Sunday at "State of the Union," Kaine also ribbed Trump for recently confusing him with a former Republican governor of New Jersey, Tom Kean.
"I was a no-show governor of New Jersey when I was governor of Virginia, and the fact that he was a lousy governor of New Jersey and he tried to raise taxes on his first day in office," Kaine jested. "Ok, look, the guy's new to it and we're a big country and there's 50 states and New Jersey's different than Virginia, I guess you've got to let him climb the learning curve."
"I don't know anything about his sanity, I've never met him," Kaine added. "But somebody who would mistake New Jersey for Virginia, or Virginia for New Jersey, I mean I just scratch my head."
Kaine: 'Nobody has given me a reason' to back TPP
On "New Day," Kaine also denied he had changed his stance on the Trans-Pacific Partnership, insisting that he has not "shifted my position on that."
Kaine voted to grant President Barack Obama fast-track authority to negotiate TPP and praised aspects of the deal, but said Friday morning that he was still concerned about an issue he raised initially with TPP: "The right of corporations to challenge unfair trade practices in private courts," without giving labor unions the same rights.
"It's been a year and nobody has given me a reason why we should embrace a trade deal," he said.
Trump has slammed both Clinton and Kaine for their past support of the TPP deal and insisted that Clinton will ultimately approve the deal after passing minor changes. Top Clinton ally Terry McAuliffe also suggested Clinton would eventually pass the trade deal as well, comments the Clinton campaign disputed.
Kaine says he's for the Hyde amendment
Kaine also said he continues to support the Hyde Amendment, which bans using taxpayer dollars for abortion.
"I have been for the Hyde Amendment. And I have not changed my position on that," he said.
Although Kaine is Catholic who is personally opposed to abortion, he has a 100% "pro-choice" rating from NARAL Pro-Choice America having voted against restrictions on abortion, including a ban on public funding for elective abortion under the Affordable Care Act and a ban on most abortions after the fifth month of pregnancy.
The 2016 Democratic Party platform calls for the repealing of the Hyde Amendment, which critics say would allow for the unlimited federal funding of elective abortions for Medicaid recipients. But Kaine recently told the Weekly Standard that he had not been informed of that change.
"I haven't been informed of that change, but I'm going to check it out," Kaine said earlier in July. "I have traditionally been a supporter of the Hyde Amendment, but I'll check it out."
Clinton's campaign manager Robby Mook and spokesman Jesse Ferguson have said Kaine supports Clinton's commitment to repeal the Hyde amendment earlier this week.
And press secretary Brian Fallon tweeted that Kaine promised to carry out Clinton's agenda on the issue.