Health minister Greg Hunt lobbied his cabinet colleague Michael Sukkar to include gender and sexuality questions in the census – despite Sukkar’s intervention to have the politically sensitive questions dumped from the census test.

In a letter to the Victorian equality minister, Martin Foley, earlier in January, Hunt revealed he had written to Sukkar, the assistant treasurer, in support of the inclusion of questions that would “greatly inform the government’s knowledge about the LGBTI+ population cohort in Australia in the 2021 census”.

Hunt’s support for the questions is significant as it is the first sign of dissent at the cabinet level over Sukkar’s position against asking Australians their gender and sexuality in the upcoming census.

Gender and sexuality questions were among eight potential new topics identified by consultation in 2018 and were set to be included in a census test late last year. In October Guardian Australia revealed the Australian Bureau of Statistics had dumped the questions from the test after intervention from the assistant treasurer’s office, prompting backlash from stakeholders including the LGBTI Health Alliance.

In December, Foley wrote to Sukkar lobbying him to include the questions. In a letter, seen by Guardian Australia, Hunt replied by saying the federal government is “committed to supporting the mental health and wellbeing of LGBTI+ people”.

“To that end I have written to the assistant treasurer to signal my support for the inclusion of questions that would greatly inform the government’s knowledge about the LGBTI+ population cohort in Australia in the 2021 census.”

He acknowledged that “LGBTI+ Australians often have unique healthcare needs and are at an increased risk of poor health outcomes and mental health issues”.

“From a health systems perspective, access to a more complete and nationally inclusive data collection would assist the Australian government to inform the development of policies that ensure access to appropriate health services for all Australians,” Hunt said.

Foley, who is also the minister for mental health, has written to concerned stakeholders noting that Hunt’s reply “suggests these issues are still under consideration” at the federal level.

Foley said he was disturbed to see “the increasingly deliberate politicisation of LGBTIQ issues in the public arena”, arguing this contributes to mental health issues for LGBTIQ people.

“We remain committed to opposing moves to wind back hard-fought discrimination protections for our LGBTIQ communities.”

Foley told Guardian Australia it is “disappointing – but sadly unsurprising – to see the [federal government] is once again divided over such an important issue, letting party politics get in the way of improving the lives of LGBTIQ Australians”.

“Not counting LGBTIQ Australians in the 2021 census would send a message that the commonwealth believes these people should remain invisible,” he said.

“We know LGBTIQ people are over-represented in poorer economic, housing, health and mental health outcomes – comprehensive demographic data would be one of the best tools we have to improve these measures, so all levels of government can tailor health and social services to better suit their needs.”

“If the commonwealth really care about suicide prevention and mental health they must take this important step in helping to reduce stigma and discrimination for LGBTIQ Australians.”

Stephen Jones, Labor’s shadow assistant treasurer, said it is clear Sukkar’s position is “driven by ideology” and Scott Morrison should intervene to ensure the questions are included.

“To do otherwise would be to deny agencies important information needed for health planning purposes,” he said. “The census can’t be a political football.”

The ABS has recommended the government not put a new question on sexual orientation into the 2021 census, despite acknowledging that two federal departments including the health department need the data to deliver services and it would have “strong value across all levels of government”.

Documents produced to the Senate reveal that despite extensive consultation with LGBTI health groups about questions on sexual orientation and gender identity and an “identified need” for sexuality data, the ABS believed the potential new topics were too sensitive and risked public backlash.

In December LGBTI Health Alliance executive director, Nicky Bath, said the ABS recommendation was “disappointing” because of the “great need” for gender and sexuality data which should be put above “the politics and individual viewpoints”.

The decision about new questions for the 2021 census will be made at cabinet level, with a decision expected to be tabled in parliament in 2020.

Since becoming prime minister in August 2018, Scott Morrison has been criticised by LGBTI equality advocates for politicising sexuality and gender identity.

Morrison has opposed sex education programs he agreed made his “skin curl” by teaching the fact of diversity in human sexuality, described teachers who support trans students as “gender whisperers” and demanded his department remove signage that gives people the choice of bathroom based on their gender identity.

Sukkar and Morrison both opposed same-sex marriage during the postal survey campaign, then abstained when the bill passed parliament. Sukkar also charged taxpayers almost $1,500 to attend a campaign rally against same-sex marriage.