Liberal and Labor MPs have sharply rebuked Senator Jacinta Nampijinpa Price's doubling down on remarks about Indian migrants on Thursday, despite initially walking them back.

During an interview on ABC's Afternoon Briefing on Wednesday, Senator Price falsely claimed Labor was deliberately bringing Indian migrants to Australia to boost its vote. She later backtracked that afternoon — but at a press conference on Thursday, told journalists she had nothing to apologise for.

"In the context of discussing the marches that took place on the weekend, it was the ABC interviewer who pushed the issue, who brought up the issue of anti-Indian migration," she said.

"What I was doing was highlighting the fact that there is huge concern for Labor's mass migration agenda, which is applying pressure to housing, to infrastructure, to services. Then I was further pursued on this line of talking.

"What I did was point out the fact that, yes, Indian migrants are the second-largest migrant group to this country, and soon to be the largest migrant group to this country. A recent Redbridge poll told us that 85 per cent of those who have Indian ancestry – and that's my children included by the way — 85 per cent voted for Labor ... So, these were the facts that I was pointing out."

Her shifting stance has forced Coalition colleagues into damage control, as Opposition Leader Sussan Ley seeks to rebuild ties with multicultural communities after the May election loss and move away from the culture wars of Peter Dutton's leadership.

As one Labor source told National Indigenous Times on Thursday that Senator Price "keep making mistake after mistake," Coalition MPs sought to distance themselves from the comments.

Appearing on ABC's Afternoon Briefing, Shadow Communications Minister Melissa McIntosh said the issue was a matter for the NT Senator but added: "I will say that I won't stick up for something that she said. This is a time where we do have issues with social cohesion and we have to be careful about what we say."

Liberal senator Dave Sharma, who has Indian heritage, told the ABC the remarks were "very poorly expressed" and said, "I don't think we should ever be going around stereotyping any migrant community for political views or beliefs".

On whether migrant groups vote as a bloc for a specific party, he added: "Never mind whatever prejudice you might reveal, but you are making a pretty deep analytical error if you think ethnic or migrant groups or professions for that matter or anything else, genders, will vote in a certain way."

Fellow Liberal senator Jane Hume described the remarks as "ill-conceived," telling the same program: "I think they were very wrong. They certainly don't represent the views of the Liberal Party or the Coalition more broadly."

She conceded the comments were unhelpful but said it was "really important that she has stepped it back".

Racist to say groups of people vote in unison

Appearing alongside Senator Hume, Labor MP Julian Hill called Senator Price's last 24 hours "bonkers".

"It was incoherent. It was all over the shop," he said. "There were literally racist tropes being spread, suggesting that all people of a particular race vote one way, as if they're Daleks with one brain cell. That is racist. It's offensive."

He then added, "I'll tell you the data: Australians of Indian heritage are more likely to be employed than your average Aussie. They work two jobs. They work hard, they contribute, just like generations of migrants before, and many of them were born here, as were their parents and their grandparents."

A transcript of ABC's Afternoon Briefing from Wednesday shows Senator Price raised the claim after host Patricia Karvelas asked whether citizens were more concerned about the core number — or the type of migrants — that are coming to Australia.

Senator Price replied: "It is definitely the core number. And of course, there is focus from this government to be getting them from particular countries over others. I think Labor like to be able to ensure that they're going to allow those in that would ultimately support their policies, their views, and vote for them as well."

When asked if she meant Labor was using migration to boost political support, she answered: "absolutely."

Pressed twice on her claims, she first said: "Those that are more Labor leaning." The second time, she added, "As we have seen, you yourself mentioned, that there is a concern with the Indian community...there's been large numbers and we can see that reflected in the way the community votes for Labor at the same time."

Appearing on the same program a day later, Indigenous Australians Minister Malarndirri McCarthy said the NT Senator's remarks were not "helpful".

"What's important here, though, is that for every politician and myself included, we have to be mindful that what we say does matter and it does resonate," she said.

"We can either be a part of calming and de-escalating the situation, or we do the reverse."