A mayor is urging Pauline Hanson to visit his community during Ramadan after the senator claimed suburbs in the area are unsafe because of its Muslim population.
The One Nation leader has been widely condemned for comments in an interview on Monday, saying there were "no good Muslims".
In a subsequent interview on Wednesday, where she walked back parts of the remarks but also rejected criticism of it, she said suburbs such as Lakemba in western Sydney were unsafe because of its Islamic residents.
"It concerns me greatly that people can't go into certain suburbs in this country now ... they don't want to go into certain suburbs and I've been there to Lakemba, you feel unwelcome," she told ABC TV.
Canterbury Bankstown Council mayor Bilal El-Hayek, who represents the area that takes in Lakemba, said Senator Hanson's comments were divisive at a time when unity was needed in the community.
"Lakemba is no different to any other suburb or shopping precinct and there is no crime issue at Lakemba," he told Sydney radio station 2GB.
"This has to stop, it really has to stop, because we need to come together at a time when the country is hurting."
The most recent census showed 61 per cent of Lakemba residents were Islamic, with the suburb hosting popular food markets at night for Ramadan.
Mr El-Hayek said he had invited Senator Hanson to attend the markets, which begin on Thursday.
"We receive over one million people, the majority are actually not of the Islamic faith," he said.
"At the moment when we need to come together, it's a shame to see people playing politics."
When pressed about her comments on Wednesday, the Queensland senator backtracked on her remarks about there being no good Muslims.
"No, I don't genuinely believe that,'' she told ABC TV, adding a non-practising Muslim woman had run for election for One Nation.
"If I've offended anyone out there that doesn't believe in Sharia law or multiple marriages or wants to bring ISIS brides in or people from Gaza who believes in the caliphate... then I apologise to you for my comment.
"But in general, that's what they want: a world caliphate and I'm not going to apologise."
Race discrimination commissioner Giridharan Sivaraman joined calls for the senator to apologise.
"Public figures have a responsibility to elevate our national conversation, not inflame tensions, divide us or undermine the dignity of others," he said.
Australian National Imams Council president Shadi Alsuleiman strongly rejected the firebrand senator's prior comments, saying they reflected a serious misunderstanding of Islam and the Muslim community.
"For many years, she has made inaccurate and harmful statements based on misinformation rather than genuine engagement," he told AAP.
Senator Hanson dismissed the criticism from Islamic groups.
"Of course they're going to say that, but I've heard more hateful things coming out of the mouths of imams giving their sermons on the streets of Sydney, and other places in Australia, but nothing's been said about that," she said.
Senator Hanson used her maiden speech to the Senate in 2016 to claim Australia was being "swamped by Muslims", a repeat of her 1996 speech to parliament's lower house about Australia "being swamped by Asians".
More recently, she drew widespread condemnation when she wore a burqa in the senate.
One Nation has been out-performing the coalition in recent surveys, with the latest Newspoll showing the party gaining a 27 per cent primary vote compared to the opposition's 18 per cent.
