Angle, in her first extended Nevada interview since winning the June 8 primary, said she was speaking broadly about the Constitution and her words about the Democratic leader were "a little strong."
The Republican nominee stopped short of an apology but said she no longer uses that phrase.
"I meant take him out of office, and taking him out of office is a little different," Angle said. "I changed my rhetoric."
Angle's interview on Nevada's KVBC's news interview program "Face to Face with Jon Ralston" came after several weeks in which she's rarely talked with reporters but turned up routinely on conservative talk radio shows. Her campaign spokesman, Jerry Stacy, said she's been busy raising money and building a campaign organization and is planning more interviews.
"We're not hiding out from anybody," Stacy said.
In a wide-ranging and sometimes contentious exchange with Ralston, Angle defended her proposal to phase out Social Security for younger workers, affirmed her opposition to abortion, including instances involving rape and incest, and sparred with the host over the origin and meaning of the separation of church and state.
When asked if separation of church and state arises out of the Constitution, Angle answered no. She said Thomas Jefferson is often misquoted and that he wanted to protect churches from being taken over by a state religion. The drafters of the Constitution "didn't mean that we couldn't bring our values to the political forum," she said.
Reid's campaign said Angle's remarks showed she believed church-state separation is unconstitutional. Angle spokesman Stacy said in a statement that Reid is "figuring out ways to twist a larger historical statement Angle was making about the origins of separation of church and state. He's doing it because he's terrified of having a real discussion about jobs and the economy."
Angle's remarks about the Second Amendment and Reid came earlier this year on a conservative radio talk show, "The Lars Larson Show." She said that "if this Congress keeps going the way it is, people are really looking toward those Second Amendment remedies and saying, 'My goodness what can we do to turn this country around? And I'll tell you the first thing we need to do is take Harry Reid out."
She did not explain what she meant by "Second Amendment remedies" in Tuesday's interview.
Reid campaign spokesman Jon Summers said, "It wasn't a gaffe, it is a philosophy. She has repeated that language many times."
Reid's campaign has been depicting Angle as too far out of the mainstream for Nevada, while she has said it's Reid who is out of step with a state suffering from record unemployment, foreclosures and bankruptcies.
At one point in the interview, Angle said the questions in the interview failed to address those larger issues in the race. "Those are things we should really be discussing," she said.