The government is set to delay a bill to improve processes for the postal survey on same-sex marriage after the Greens and marriage equality advocates warned that passing it may undermine the high court challenge against the vote.

Guardian Australia understands that the Human Rights Law Centre, representing Australian Marriage Equality and the Greens LGBTI spokeswoman Janet Rice in the challenge, has advised that passing a bill to set rules for the survey run by the Australian Bureau of Statistics could harm their chances in court.

Marriage equality advocates are to write to Labor, the Greens and crossbench warning them not to pass any bill prematurely. The Greens have already written to the government urging it to delay legislation.

On Wednesday the acting special minister of state, Mathias Cormann, told Guardian Australia: “The most likely timing for consideration of a bill to provide for additional legal safeguards ... to support the fair and proper conduct of [the survey] will be after the high court’s hearings on 5 and 6 September.”

On Friday the Cormann contacted Labor and the Greens, offering to extend electoral law provisions for authorisations of ads and banning misleading information, fraud, bribery and intimidation to protect the survey.

At first the government suggested the bill could be presented to parliament this week. It has given the bill to Labor, which is considering its position, and crossbench parties.

No details of the bill are publicly available but Guardian Australia understands it extends basic electoral protections and goes no further.

On Wednesday Rice told Guardian Australia: “We are concerned about the potential interaction of this legislation with the high court challenge so we have informed the government that our strong preference is for this legislation to be considered after the challenge is concluded.”

Rice said human rights “should not be put to a public vote” and described the plebiscite as a “hurtful waste of time” because, ultimately, parliament would have to vote to change the law.

On Sunday the shadow attorney general, Mark Dreyfus, raised the issue that passing a bill could have an impact on the cases, set to be heard on 5 and 6 September, just a week before ballots are due to be mailed on 12 September.

The constitutional law expert George Williams agreed, warning it could undermine the challenge.

“A key part of the case is that the executive doesn’t have parliamentary support [for the postal vote] … if new legislation expressly or impliedly provided support it could take the wind out of the sails of the challenge,” Williams said.

“[Labor and the Greens] have rejected legislation for the [compulsory] plebiscite. If they want to maintain the strength of the high court challenge, they should exercise caution with whatever legislation might be seen to support the postal vote.”

On Wednesday Guardian Australia learned that legal advice from the HRLC aligns with Williams’ concerns, and AME will urge its allies in parliament to block any attempt to fix the postal survey this week.

Cormann issued a statement on Wednesday saying he had made a new direction to address a reported loophole that could have allowed 16- and 17-year-olds to vote in the postal survey.

He quoted the Australian Electoral Commission, saying 16- and 17-year-olds would never have been able to vote because they are only provisionally enrolled.

Nevertheless, he issued a new direction to the ABS “to make the intention absolutely clear” that only Australians who are 18 years or older on 24 August 2017 will be allowed to vote.

Labor and pro-marriage equality Coalition members have started to campaign for a yes vote. A Labor website declares “It’s Time for Marriage Equality”, echoing its successful 1972 federal election slogan. Coalition members have started a website, Lib Nats for Yes.

The national director of Libs & Nats for Yes, Andrew Bragg, told Guardian Australia his group was “collecting information [from volunteers] to support the campaign”.

He said the information “will be solely preserved for the campaign” and “will not be passed on” to the Liberal party or other third parties.

The Labor website contains a Labor party authorisation and links to policy that states information gathered “is also used to communicate with you about various material”.