"Every president since Richard Nixon, and including Nixon. Now he was not known for the most elevated ethical standards," said Kaine, the Democratic vice presidential nominee, at a Manchester, New Hampshire, campaign organizing event.
"But I will say, even Richard Nixon released his tax returns to the public when he was running for president. Because, he said -- as has every major party nominee of both parties since -- the American public have a right to see my tax returns."
"He says the rules that apply to everybody else do not apply to Donald J. Trump," the Virginia senator said.
Kaine and his wife released ten years of tax returns on Friday, and Democratic presidential nominee Hillary Clinton has released tax returns dating back to 1977.
Kaine on Saturday cast doubt on the contents of Trump's tax returns: "What doesn't he want to show?" he asked, citing Washington Post reporting that was not able to verify Trump's claimed $20 million gift to St. Jude's Children's Hospital.
"We might find that this generosity that he's claiming, is -- is just smoke and mirrors. I think that's probably the case," Kaine said.
Clinton's running mate called out Trump for "[bragging] about using every trick" to avoid paying taxes, citing a "couple of instances" in the 1980s and 1990s where he "paid no taxes" at all.
"He says he's gonna be a great commander in chief for the military. Who supports the military? We pay taxes to support the military," Kaine said, adding that the billionaire is "trying to dodge supporting our veterans" by not paying his fair share of taxes.
When prompted by an audience member, Kaine also noted that Trump's tax returns "might show investments connected to people we have questions about."
He added that voters should ask how much the businessman would benefit by his own tax plan.
"You are proposing a tax plan that is going to benefit Donald J. Trump more than anyone else," Kaine said. "That's a fundamental character question."
This isn't the first time Trump has come under fire for his refusal to release his tax returns.
Upon releasing his own tax returns in February, Sen. Ted Cruz said it was time for his GOP primary rival to "stop the excuses."
"If Donald is embarrassed about his tax returns, it's up to the voters to assess the facts," Cruz said in a statement at the time.