Story highlights Sen. Tim Kaine moved to dispel concerns from the left as he voiced his support for abortion rights

Kaine is Catholic and personally opposes abortion -- but he says he supports a woman's right to choose

Washington (CNN) Virginia Sen. Tim Kaine says that he's a staunch backer of abortion rights, remarks that could dispel concerns from the left as Hillary Clinton considers him as a possible running mate.

In an interview in the Capitol, Kaine -- a Catholic who personally opposes abortion -- says his views on the issue have not changed over his career. But asked if he would characterize himself as "pro-life," he said: "I've never embraced labels."

"I have a traditional Catholic personal position, but I am very strongly supportive that women should make these decisions and government shouldn't intrude," Kaine told CNN. "I'm a strong supporter of Roe v. Wade and women being able to make these decisions. In government, we have enough things to worry about. We don't need to make people's reproductive decisions for them."

Kaine's comments come as Clinton's VP selection process is entering its final stretch, with an announcement expected next week after the Republican National Convention concludes.

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