Angus Taylor has attempted to clarify comments on multiculturalism after his five non-answers on Tuesday which left colleagues dumfounded and questioning the opposition leader’s approach to One Nation.

As senior Liberals lined up endorse to Australia’s cultural diversity on Wednesday, outspoken backbencher, Andrew McLachlan, went further, challenging his leader to “embrace the reality of modern Australia”.

“If you aspire to lead our nation you should embrace the reality of modern Australia,” the Liberal senator told Guardian Australia.

“It is a prerequisite of a leader to fight for the aspirations of each and every member of our community.”

Taylor, in a press conference on Tuesday, repeatedly refused to say whether he supports multiculturalism in Australia, sidestepping questions about his views, and claiming “there’s all these vague words running around” before asking a reporter, “Do you want to define it for me?”

The line of questioning was in response to One Nation leader Pauline Hanson last week declaring that Australia “cannot be a multicultural society” and must be “monocultural”.

The opposition leader’s answers were met with surprise and concern from some Liberal colleagues, who saw Hanson’s “monoculture” claim as crossing a red line and gifting the Coalition a clear opportunity to differentiate themselves from One Nation’s agenda.

“Nobody knows what monoculture means and it won’t resonate. The fact he [Taylor] didn’t have any answer struck a bit of a confidence blow. Instead of capitalising on [Hanson’s] errors, he is just tip-toeing,” one Liberal MP said.

The Liberal said MPs across the factional divide were becoming “exceptionally uncomfortable” with the strategy of attempting to compete with, or even outflank, One Nation on issues such as immigration.

In a statement late on Tuesday, Taylor indicated he did support multiculturalism in some form.

“I believe in an Australia where everyone respects our laws, shares our values and contributes to the fabric of our country. That is the type of multiculturalism that we believe in. We reject Labor’s multiculturalism which sees different people held to different standards because of their cultural background,” he said.

“That is how we have ended up with antisemitic hatred on our streets, ugly protests on the Harbour Bridge, terrorist sympathisers back into our community and non-citizens accessing benefits that should be there for Australians.”

The statement mirrors new “talking points” that have been issued to Liberals MP to help them respond to media questions on the subject.

Taylor’s comments on Tuesday were ridiculed by Labor in parliament, with the treasurer, Jim Chalmers, claiming: “One of the reasons why the Liberal party is dying in [Taylor’s] arms is because his efforts to out–One Nation One Nation are becoming increasingly pathetic.”

In an interview with Guardian Australia after Hanson’s press club speech, the Liberal MP, Garth Hamilton, challenged the One Nation leader to explain how a “monoculture” would be enforced.

“Is a bulldozer going to be driven through Chinatown? Can I run a kebab shop? Can I go to the [Greek] Paniyiri festival? When the Russian ballet comes out, can I go watch that? I know this sounds ridiculous. Answer these freaking questions, Pauline,” he said.

“We’ve never been a monoculture.”

Some Liberals suspect Taylor’s equivocation on multiculturalism is in part influenced by Tony Abbott, who issued a tacit endorsement of Hanson’s position in a Sky News interview aired overnight.

“Australia has a core Anglo-Celtic culture. We have a foundational Judeo-Christian ethos that should never change,” the former prime minister and now Liberal party president said.

McLachlan said Abbott’s “philosophical musings unhelpful and deny the realities of modern Australia”.

“Abbott should focus on building our campaign capability and organisational strength. Not trying to build a Tardis to take us to a time and place that never was.”

On Wednesday, the deputy Liberal leader, Jane Hume, said she didn’t agree with “the politics of identity of the left” but also rejected “the policy of cultural fear from the right”.

“We are a multicultural society. Let’s face it, we already are. I had my three children christened in an Anglican church. My mother goes to Catholic church on Sundays, and I go to Greek Easter and crack little red-dyed eggs,” she said.

“I don’t really care where you came from. I don’t give two hoots what your country of origin is. What I care about is whether you’re going to contribute to building our nation.”

Senator Maria Kovacic, the daughter of Croatian migrants, said Australia was “a beautiful multicultural society” which was “been built on the backs of many different migrants over the past 200 years”.

Anne Ruston said Australia was “built on multiculturalism”.