The federal Liberal party believes it has "cauterised the wound" caused by the furore around Indian migrants, after leader Sussan Ley dumped a popular conservative senator from shadow cabinet.

But the opposition leader has been criticised for the way she managed Jacinta Nampijinpa Price after the Northern Territory senator suggested last week that the government favoured Indian migrants because they vote Labor.

It culminated in the senator being sacked from the frontbench on Wednesday after she did not, when repeatedly asked, declare her confidence in Ms Ley's leadership.

She had already rejected earlier calls from her colleagues to apologise for her comments, which infuriated the Indian community.

The senator has maintained she was trying to make a point on "mass migration" under Labo

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