Fatima Payman says people should not assume her religion was the reason she quit Labor over its stance on Palestine

Fatima Payman has warned about pigeonholing her as just a Muslim senator who only cares about Palestinian rights and freedoms after she quit the Labor Party to take a principled stance on the issue.

Senator Payman has moved to the crossbench rather than give her seat back to Labor, pointing to other topics such as Indigenous incarceration and mental health she was passionate about and felt the government could go further on.

The West Australian branded suggestions her defection was purely a result of her religion as insulting.

Taking a stronger stance to support people in Gaza and action against Israel was a human rights issue, she said, pointing to reports 38,000 people had been killed in the besieged enclave and Israeli occupation in Palestinian territories.

Senator Payman rubbished suggestions that because she had met with people from a grassroots Muslim organisation set to run candidates in some Labor electorates meant she was going to join or start her own party.

'It's unfortunate that the stereotyping is so deep rooted in, perhaps this institution (politics), but also in our media structures,' she told AAP.

'They're quick to assume that just because I've met with a Muslim group ... that now I'm going to go off and form a Muslim party.

'I've also met with the Jewish Council of Australia, I've met with Christian groups ... but the fact that you would only hone in on that, it's very disappointing in today's day and age.'

Diversity and multiculturalism needed to be celebrated 'but we don't pigeonhole', she said.

'It feels like now I have to go around defending why I've met with a particular community group, like it's just bizarre,' she said.

'I mean, they wouldn't ask that question of a middle-aged Anglo-Saxon man who chooses to leave.'

The former Labor senator sensationally quit the party in a hastily called press conference at Parliament House on Thursday.

She had raised the recognition of Palestine - which Labor has affirmed to do but with no timeline and some caveats - with the prime minister and senior ministers but was unable to secure change, Senator Payman said.

Timely recognition was needed to put pressure on Israel to 'cease its onslaught' in Gaza and was something she told political leaders she couldn't compromise on,' she said. 

Prime Minister Anthony Albanese suggested the senator had been cooking up a political plan for more than a month, seizing on her meetings with a political strategist and the community group last week.

Her decision to cross the floor - which can lead to expulsion in the Labor Party - and then quit the party were made at the last minute, she said.

The Australia Palestine Advocacy Network welcomed her decision as did Labor Friends of Palestine NSW, made up of rank and file members, who expressed sorrow.

The defection exposed a fault line within Labor that Muslim voters who supported the party for its anti-racist immigration and social policies could consider it becoming more pro-Israel, political expert Stewart Jackson said.