Greens deputy leader Mehreen Faruqi has repeatedly refused to answer whether she believes 'Hamas should be dismantled,' arguing it's not up to her to say 'who should be gone or not'.
Ms Faruqi appeared on ABC's Insiders on Sunday morning following the party's failed attempt to have parliament recognise Palestinian statehood this week.
The issue saw now-independent senator Fatima Payman resign from Labor after being frozen out when she crossed party lines to side with the Greens.
Ms Faruqi called out Prime Minister Anthony Albanese and his government for not supporting the motion without adding 'caveats'.
When grilled on her stance however, Ms Faruqi could not say whether she wanted Hamas to be abolished as a condition to statehood.
The NSW senator was asked five times whether the Islamic terrorist group responsible for the October 7 attacks needed to be either removed or disbanded.
'Hamas has nothing to do with recognising Palestinian statehood,' she told host David Speers.
'Recognising Palestinian statehood is about Palestinians being able to self-determine.'
When questioned further on the issue, the senator said: 'I can't keep repeating it again and again, (Hamas) has nothing to do with Palestinian statehood'.
'Palestinians need to decide where they want to go with their own region, not intervention from western countries.'
Speers noted Hamas is listed in Australia as a terrorist organisation and told the senator 'surely you're able to say whether you'd like to see them gone or not'.
'It's not up to me to say who should be gone or not,' she replied.
Ms Faruqi said she couldn't answer the question because it's based on a 'hypothetical situation' if Palestinians were to be granted statehood.
She then turned her attention towards the Albanese Government who pulled support after their proposed amendments to the bill weren't taken on board.
Foreign Affairs Minister Penny Wong said the government would have supported the motion if Palestinian recognition was 'part of a peace process in support of a two-state solution and a just and enduring peace'.
Ms Wong later told reporters that the Greens motion was strictly 'all about politics, not about change'.
Ms Faruqi hit back at the claim and said she was 'really sick and tired of being gaslighted (sic) in that Parliament by the Labor Party'.
'I was flabbergasted that Labor wants to talk about peace while doing absolutely nothing.'
Opposing the Greens' motion caused headaches for Labor with pro-Palestine protestors taking to Parliament House on Thursday.
The protestors climbed to the roof of the capital building and unfurled banners of popular chants for the pro-Palestine movement, one including a Hamas symbol.
'That upside down red triangle is Hamas-symbology that is supposed to indicate IDF targets and Israeli targets in the context of the war in Israel and Gaza,' Liberal Senator James Paterson said.
The party was left with one less seat in the upper house just hours later when WA senator Fatima Payman announced she was resigning to become an independent senator.
Ms Payman was suspended indefinitely from her party's caucus meetings last Sunday after she revealed she'd have no qualms crossing the floor again on motions involving Palestine.
The attention given to the rift within the ALP took steam out of Mr Albanese's tax cuts and cost of living measures the government has introduced.
Prime Minister Anthony Albanese on Friday blasted Senator Payman's decision to leave Labor and warned parties against going 'down the road of faith-based political parties' because it undermines social cohesion.