Australians in favour of an Indigenous voice to parliament are in the minority as support for the constitutional change drops in a major poll.

The share of people nationally who approve of enshrining the voice in the constitution has dropped to 49 per cent, down from 53 per cent in May, according to a Resolve Strategic survey.

The poll of 1606 voters, published by Nine newspapers late on Monday, is the first significant national poll to show the ‘no’ side leading.

But its findings are contradicted by a Guardian Essential poll, published on Tuesday, which found 60 per cent of people were in favour of the voice, up one percentage point on the previous survey.

The survey of 1123 voters showed 40 per cent of respondents were opposed to the change.

The referendum is expected to be held between October and December.

The debate on the voice constitutional alteration bill, which is in the Senate, is expected to last all week.

A possible vote might take place at the end of the week, with the Senate sitting on Friday.

The Greens will not support their former senator Lidia Thorpe’s amendment to the legislation, which aims to add more detail about preventing the sovereignty of Indigenous people from being ceded.

The party described the amendment as a poison pill that will help the referendum fail.

Instead, Greens senator Dorinda Cox will propose an amendment which acknowledges sovereignty was never ceded.

The poll figures come as the Yes 23 Campaign hails the support of more than 500 organisations, from charities to business, faith and multicultural groups, as backing a ‘yes’ vote.

The Resolve poll said those supporting the ‘no’ case were in the majority in three states, Queensland, Western Australia and South Australia.

The national ‘yes’ figure has steadily dropped from a peak of 64 per cent support in a September 2022 Resolve survey.

The latest survey showed 18 per cent of voters were undecided, while 42 per cent were firmly in favour and 40 per cent against.

But when those who were undecided were asked to answer only ‘yes’ or ‘no’, as they would in a referendum, the ‘no’ vote had a slender lead.

Yes 23 Campaign director Dean Parkin said voice supporters continued to hit the phones and hold events to encourage people to get behind the constitutional change.

“This is about bringing all Australians together,” he said.

“We are building a positive movement that includes people from all walks of life.”

By Peter Bodkin and Tess Ikonomou in Canberra