Liberal senator Jacinta Nampijinpa Price has been stood down from the shadow front bench after a chaotic week in which she refused to apologise over accusing Labor of importing Indian migrants to boost their vote.

Hours after a press conference where she refused to back Opposition leader Sussan Ley, Senator Price said she had been stood down from the shadow ministry.

"I have accepted the Leader's decision. And I reiterated my regret in not being clearer in my comments on the ABC last Wednesday," she said in a statement

"Nevertheless, I took the opportunity to express to the Leader my disappointment that some colleagues disregarded the key point I was making about the damaging impacts of mass migration. And that some colleagues instead chose to indulge agenda-driven media commentary on this matter."

The controversy has placed the Liberal Party in damage control, with MPs distancing themselves from Senator Price's comments and others urging her to apologise. It has also created new challenges for Ms Ley, who is attempting to rebuild trust with multicultural communities and move the party away from the anti-migrant stance associated with former leader Peter Dutton.

Senator Price said in her statement that her comments, where she expressed concern about migration, was simply echoing those of "millions of Australians".

"My concern is not migration itself – it's the magnitude of migration. Migration at the current scale and pace is putting excessive pressures on housing, infrastructure and services. And that makes life tougher for all families. I want to see a better life for all families – whether you're a migrant, a resident, or a citizen – and regardless of your background," she said.

"This has been a disappointing episode for the Liberal Party. I will learn from it. I'm sure others will too. No individual is bigger than a party. And I'm sure events of the past week will ultimately make our party stronger."

In her original comments last week, Senator Price falsely accused the government of bringing in migrants "from particular countries over others" to secure votes, citing the Indian community as an example.

She rapidly issued a clarification — reportedly after pressure from Liberal leadership — saying Australia's migration policy was non-discriminatory and that "suggestions otherwise are a mistake" — but she stopped short of apologising.

The following day, she then told reporters she had "nothing to apologise for," insisting it was "the ABC interviewer who pushed the issue — who brought up the issue of anti-Indian migration".

"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," she said.

She also pointed to polling data: "A recent Redbridge poll told us that 85 per cent of those who have Indian ancestry… 85 per cent voted for Labor."

Pressure has continued to mount within the Coalition for Senator Price to apologise. Some colleagues, including Liberal frontbencher Julian Leeser, issued their own statements of regret.

"I want to apologise to the Indian community for any offence they felt from recent comments made by one of my colleagues," Mr Leeser wrote on social media.

Nationals Senator Bridget McKenzie also called on Senator Price to do the "appropriate, responsible thing" and apologise.

Speaking in Perth on Wednesday, Senator Price admitted her remarks last week on ABC Afternoon Briefing were "clumsy," but insisted she would not be silenced on the issue of migration.

"Last week, I made comments on the ABC. I almost immediately clarified those comments and expressed, of course, the fact that while, you know, my comments were certainly clumsy, unfortunately, the issue that's of great concern, which I won't be silenced on, is the issue of mass migration in our country," she said.

"That was the prime issue that I was talking about, and continue to talk about, and an issue that I truly believe that we need to be able to have a respectful debate about, and we should all be focused on that now."