"He appears not to be conflicted with our public policies mirroring the Ten Commandments with regard to stealing, perjury, or forms of murder, other than abortion," he added.
In the debate, Kaine countered Republican presidential candidate Donald Trump's early comments, later retracted, that women should be punished for having an abortion.
"Before Roe v. Wade, states could pass criminal laws… to punish women if they made the choice to terminate a pregnancy," Kaine said.
According to Archbishop Naumann, decades of legal history show that this was "certainly not the case."
"The laws were enforced against the abortionists," he said. "Our own legal experience shows clearly that it is possible to develop public policies aimed at protecting children, not punishing women."
The archbishop invited Kaine to speak with women who have had abortions and have sought the assistance of Project Rachel and other post-abortion ministries that help women and men find "healing, hope and mercy after an abortion."
He blamed permissive abortion policy for placing the entire burden of an abortion decision upon the woman.
Archbishop Naumann noted Kaine's expression of anguish when he enforced death sentences as governor and the impression that Kaine attempted to convince Virginians to abolish the death penalty.
But he said Kaine seems not to have made a similar effort to convince Virginians "to work for public policies that protect the lives of the unborn."
"Instead, he appears eager to champion not only maintaining the status quo, but actually expanding abortion rights," the archbishop charged.
Archbishop Naumann also acknowledged the tensions of the 2016 election year.
(Story continues below)
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"This presidential election presents all Americans with a difficult choice. Both major political parties have nominated very flawed candidates," he said.
He encouraged voters to think not only of the presidential candidate, but who they will appoint to "key Cabinet and other powerful government positions … We are choosing not just a president, but an entire administration," he said.
The archbishop conclude by advising voters to "be wary of candidates who assume to take upon themselves the role of defining what Catholics believe or should believe. Unfortunately, the vice-presidential debate revealed that the Catholic running for the second highest office in our land is an orthodox member of his party, fully embracing his party's platform, but a cafeteria Catholic, picking and choosing the teachings of the Catholic Church that are politically convenient."