Almost three-quarters of eligible Australians have voted in the same-sex marriage postal survey, according to the Australian Bureau of Statistics estimate released on Tuesday.

The ABS estimates that 74.5% of enrolled Australians, or 11.9m people, had returned their survey forms by Friday. The figure is a 7% increase on last week’s estimate that 67.5% of Australians had voted.

“With form scanning now well under way, this estimate is based on a count of forms scanned rather than earlier estimates that were based on the weight of the bulk containers of returned forms waiting to be scanned,” the ABS said in a statement.

The ABS estimated that it had received an additional 300,000 forms last week.

The figure is consistent with the Guardian Essential poll released on Tuesday, which found that 75% of Australians had voted in the postal survey. Given the consistent lead the yes side has held in public opinion polls, higher turnout is believed to make a win for marriage equality more likely.

The new survey of 1,859 voters records 60% saying they have voted yes, which is down 4% from the last time the question was asked three weeks ago, and 34% saying they have voted no, which is up 4% in the same timeframe.

Equality Campaign executive director, Tiernan Brady, said the turnout figures were “fantastic” because they “show the people understand how important marriage equality is and the power of their vote” in getting parliament to change the law.

“In these final days we still have no room for complacency and we call on all voters, especially younger voters, to make sure their voice is heard,” he said.

Although there were some concerns in the government that this sitting week could provide an opportunity for a boilover on marriage equality and religious freedom, neither issue was raised in the Coalition party room on Tuesday.

Conservatives are working on their own marriage bill but have not publicly trumpeted the effort because they do not wish to appear defeatist before voting closes on 7 November and the ABS announces the result on 15 November.

On Saturday the no campaign’s Coalition for Marriage pushed for broad exemptions to discrimination law to allow service providers to refuse any weddings that send “a message with which they disagree”, prompting concerns from marriage equality advocates that such a stance would allow discrimination on any basis. Read more via the Guardian