Speaking to CNN's Erin Burnett on "OutFront," Pence was referring to comments made earlier in the day by Senate Minority Leader Harry Reid, who on the Senate floor called Trump
a "spoiled brat," "a con artist" and a "human leech who will bleed the country."
"I think those remarks are beneath the dignity of the United States Senate," Pence said. "Look, to be honest with you, I'm starting to get a whiff of desperation from the other side. It seems like the attacks are getting a little more intense."
Pence defended Trump's recent comments
about Federal Reserve Chair Janet Yellen, whom Trump accused of keeping interest rates low and creating a "false stock market" in order to help President Barack Obama.
The Indiana governor declined to accuse Yellen of political gamesmanship, but said he had a hard time figuring out the Fed's policies.
"I think it's hard to understand why the Fed continues to advance policies that really work for hedge fund managers on Wall Street, here in New York City, but really aren't working for working families on Main Street," Pence said. "I think Donald Trump is saying that it's time that we brought forward the kind of economic policies that will allow interest rates to return to a rational point."
He added, "I just think it's very curious to see the Federal Reserve continue to resist efforts to respond in the marketplace in a way that puts the interest of middle class families first."
Trump's tax returns
Asked about Trump's tax returns -- which the GOP nominee has refused to release -- Pence reiterated the campaign's stance that voters won't see them until the conclusion of what Trump has said is an ongoing IRS audit.
"I don't hear a lot of people talking about tax returns," he said. "I think he's been very forthcoming about saying that he'll reveal those tax returns when a routine audit is done."
Pence maintained that voters curious about learning more about Trump's financial dealings already have that information available.
"What your viewers ought to know is that both Donald Trump and I, and frankly the other two major party candidates in this race, have all filed the full financial disclosure that federal law requires," Pence said. "And people that want to learn about Donald Trump's financial interests can read over 100 pages of disclosure online right now at the Federal Election Commission. And I encourage people that are curious to do that. Those tax returns will be coming when that routine audit is done."
Defends Donald Jr.
Pence also defended Donald Trump Jr.'s controversial comments earlier Thursday when he referred to "warming up the gas chamber"
in complaining about the treatment his father has received from the media compared to its coverage of Democratic nominee Hillary Clinton.
"Well, clearly he was talking about capitol punishment and not making reference to that awful period of history we know to be the Holocaust," Pence said. "But look, his point is well made beyond whatever rhetoric he chose to use."
Walks back child care comments
When asked about Trump's new child care plan that the businessman unveiled on Tuesday with the help of his daughter Ivanka, Pence said that it's Trump's "appreciation for the role of working women."
Pence also defended his 1997 remarks when he wrote, "The daycare kids get the short end of the emotional stick," saying that he has since changed his mind about the issue.
"That was probably a real long time ago ... I think I still had dark hair back then, Erin ... I will always believe that the best child care is an is in the home where a family that has the means to be able to provide that," Pence said, adding, "But we have some world-class child care in our country today."