Mr Taylor has clarified his stance after failing to answer four questions about whether he supported multiculturalism during a media conference on Tuesday.
His comments follow One Nation Leader Pauline Hanson's call for Australia to adopt a "monoculture".
"We need every Australian to believe in our system of law, to believe in our basic freedoms, to believe in our parliamentary democracy, and people have been coming to this country in recent times who do not believe in those things," Mr Taylor told Sydney's 2GB Radio on Wednesday.
"Making sure that people who come to this country contribute to this country and commit to it, that's not a monoculture ... but it is requiring that people adopt Australian values. They are not welcome if they're not prepared to do that.
"Call that whatever you like, but I just think that's common sense... you know, it is a version of multiculturalism."
The opposition leader said his view of multiculturalism differed to Labor's approach, where people of any culture, including "ISIS culture", could enter Australia.
An exasperated deputy Liberal leader Jane Hume, from the party's moderate wing, said Australia was already clearly a multicultural society.
"This is a ridiculous argument. I can't believe we've managed to get ourselves into this," she told reporters in Canberra.
"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 Hume denied Mr Taylor's comments had hurt the coalition's standing in diverse communities, claiming they were more concerned about the government's changes to tax on investments.
Senator Hume insisted she was "pretty aligned" with Mr Taylor, but when pressed said reporters should direct their questions to the opposition leader.
The opposition leader also said he had arrested his party's decline in the polls since taking over the top job, despite One Nation continuing to cannibalise the coalition's vote.
"It was collapsing at a rapid, rapid pace... I look forward, not backwards, and I think the country wants me to look forward," he said.
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