Liberal leader Sussan Ley has been forced into damage control after Senator Jacinta Nampijinpa Price said Labor was letting lots of Indians into Australia to shore up their vote.

Price made the comments in the aftermath of the weekend’s anti-immigration marches attended by neo-Nazis.

She told ABC TV on Wednesday afternoon that the protests were fuelled by concerns about migration.

Pointing to the Indian diaspora, she claimed Labor “allow those in that would support their policies”.

“It is definitely the core number. And of course, there is focus from this government to be getting them from particular countries over others,” Price told ABC’s Afternoon Briefing.

“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.”

Price has refused to apologise, but later she “corrected” her comments.

One Nation Leader Pauline Hanson puts on an Australian Flag in the Senate chamber. Photo: Mike Bowers

On Thursday, Ley reiterated support for the Indian community while insisting the Coalition’s migration policy was non-discriminatory.

“I’m fighting for every single Australian, no matter where you came from, and our Australian Indian community are amazing,” Ley told Sky News.

“You contribute, as Australian Indians, so much to our country.

“We know how hard you work, your family values and the contribution you make across this country and as opposition leader, I value that incredibly.”

An hour after Wednesday’s broadcast, Price issued a statement clarifying her remarks.

“Australia maintains a longstanding and bipartisan non-discriminatory migration policy. Suggestions otherwise are a mistake,” she said.

“My remarks were made in a wide-ranging interview on ABC where I sought to highlight issues of uncontrolled mass migration and ruptures to social cohesion.”

Ley said Price had “corrected” her comments, but the NT senator doubled down on Thursday.

“I don’t believe I have anything to apologise about,” she said in Canberra.

Price’s comments came only hours after she had draped herself in the Australian flag in the Senate – a move copied by One Nation leader Pauline Hanson soon after.

Shadow attorney-general Julian Leeser said the Coalition believed in a “race-blind” migration policy and paid tribute to how the Indian community had contributed to Australian history, noting some had served the Australian Imperial Force in World War I.

“These people love Australia,” he told ABC radio.

“They loved it enough to give their lives for it – that’s the same that Indian Australians are doing today and I think they make a wonderful contribution.”

Racism was on full display at Sunday’s anti-immigration rallies, with flyers for the events using false claims to fuel anti-Indian rhetoric.

Members of the far right spoke at some protests, and in Melbourne, prominent neo-Nazi and white nationalist Thomas Sewell has been charged after he and about 40 men dressed in black allegedly stormed Camp Sovereignty after Sunday’s rally.

Though the actions of neo-Nazis have been widely condemned across the political spectrum, members of both major parties said not everyone who marched on Sunday was affiliated with the far right.

Labor has pointed the finger at the opposition for stoking community division and using migrants as scapegoats while the opposition claimed the government’s approach to migration had been “rushed and chaotic”.

Independent senator David Pocock condemned Price’s remarks and urged politicians to foster social cohesion.

“The comments are so divisive and damaging to a country that should pride itself on being multicultural,” he said.

“I would urge members of this place to really reflect on the way that this debate is being handled.”

-with AAP