Jacinta Nampijinpa Price appeared on an episode of the conservative 2 Worlds Collide podcast, where the host suggested immigrants are "flooding" Australia.
Podcast host and military veteran Sam Bamford said on the episode he felt the government was ignoring that "Australia is for Australians".
"We've got to stop this," he said, after suggesting earlier in the podcast that immigrants were "raiding" the homes of veterans.
"We can't keep flooding us with hundreds of thousands of Indians, Chinese, Africans, Middle Easterns and Gazans," he said.
A video of the 72-minute podcast, posted to YouTube on Thursday, shows Senator Nampijinpa Price nodding and making affirmative noises to Mr Bamford's points.
Mr Bamford then said he had just outlined "a lot of information" before asking Senator Nampijinpa Price for her thoughts.
She replied: "Yeah, absolutely. I totally agree.
"I mean if people want to come to Australia, they have to adopt our values, full stop," she said.
Mr Taylor said it was very clear the senator agreed with the position of the Liberal Party.
"We shouldn't discriminate on immigration based on race or ethnicity or religion, but we should based on values," Mr Taylor said.
"People who come to this country should share our core values, and we ask them to do that in the citizenship ceremony."
Senator Nampijinpa Price issued a statement suggesting she did not agree with all of Mr Bamford's comments.
"On the 2 Worlds Collide podcast I was asked a nearly 700-word, wide-ranging question covering multiple issues, which the interviewer himself concluded by saying: 'I mean that's a lot of information' - and I agreed that it was," she said.
"My response was to that remark. It was not intended as an endorsement of every point raised across a lengthy monologue.
"The broader discussion was about migration pressures, housing and social cohesion.
"I was very specific in my remarks that people who come to Australia should adopt Australian values, contribute positively and support social cohesion."
Senator Nampijinpa Price said in the podcast that immigrants, including Chinese people during the gold rush, and Italian and Greek migrants in the 1970s, were part of Australia's make-up.
"So many Australians have such a mixed heritage, ethnically. Fundamentally, it comes down to our values," she said.
Labor MPs including minister Anne Aly and backbencher Julian Hill are calling for Senator Nampijinpa Price to be stood down from her position over the comments.
"No Australian should … have to deal with the Liberal Party constantly punching down and questioning their existence and contribution to our nation," Dr Aly posted on social media.
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