An influential crossbench senator says Gladys Liu has "reached the Sam Dastyari threshold" after admitting she was a member of a Chinese propaganda organisation.
Liberal backbench MP Gladys Liu has been urged to consider her future in the Parliament as questions persist about her loyalty to Australia.
The Hong Kong-born MP, who was elected in May, admitted on Wednesday that she had been a member of the Guangdong Overseas Exchange Association, after earlier saying she could not recall if she had been involved.
Centre Alliance Senator Rex Patrick said she had not been transparent about her links to Chinese organisations.
"She's reached the Sam Dastyari threshold where she must consider her tenure," Senator Patrick told ABC radio, in a reference to the former Labor MP who was forced to resign over his dealings with Chinese businessmen.
But Prime Minister Scott Morrison is standing by the embattled Victorian MP.
Senator Patrick called on the PM to seek advice from Australia's security agencies.
"If there are deep long-standing connections back into the Communist Party that raises a definite concern," he said.
"It is an important national security issue and the prime minister must show leadership on it."
But Senator Patrick, who is one of six crossbenchers the government regularly negotiates with to pass legislation, said the issue would not sour his relationship with the government.
In a statement issued on Wednesday, Ms Liu insisted she was a "proud Australian" and had resigned from several Chinese community and business organisations.
"Unfortunately, some Chinese associations appoint people to honorary positions without their knowledge or permission," she said.
"I do not wish my name to be used in any of these associations and I ask them to stop using my name.
"I have resigned from many organisations and I am in the process of auditing any organisations who may have added me as a member without my knowledge or consent."
Uncomfortable with Chinese heritage focus
Government Minister Greg Hunt has questioned the motives of some critics of Ms Liu, the first Chinese-born MP elected to federal parliament.
"I am very uncomfortable with the way that some people have focused on her Chinese heritage, the fact that she has an accent," Mr Hunt told reporters on Thursday.
He expressed confidence in Ms Liu as a fit and proper person to be in the Parliament.
Senior Liberals were reportedly warned by the intelligence community about Ms Liu's links to China prior to her preselection in Chisholm in 2018.
Mr Hunt said he was not one of them and was unaware of such a briefing.
Labor deputy leader Richard Marles said serious allegations had been made and called on the prime minister to respond.
"It is for the PM to act, the PM needs to be fronting the Australian people and making it really clear what his position is," Mr Marles said.