Polling for The Sydney Morning Herald and The Age shows the coalition’s female primary vote has fallen from 41 to 37 per cent since the last federal election in May 2019.

Support for Labor among women rose two percentage points to 35, while female backing for independents lifted from four to seven per cent.

The findings come during renewed debate about the treatment of women in the Liberal Party after former MP Julia Banks accused the prime minister of menacing behaviour.

Through a spokesman, Morrison has denied the claims.

According to the research, the coalition’s overall primary vote has fallen from 41 to 39 per cent nationwide since the election.

A separate Guardian Essential poll shows the prime minister suffered a six percentage point hit to his approval rating which has fallen to 51 per cent, its lowest in 12 months.

One in three people surveyed rate the federal government’s response to coronavirus as poor, rising from 24 per cent a month ago.

That is the highest figure since the start of the pandemic while the number giving the COVID response a positive rating is at its lowest, sharply falling nine points to 44 per cent.

Labor leader Anthony Albanese’s approval rating grew slightly to 41 per cent but he remains well behind in the preferred prime minister stakes in both polls.

The Essential survey of almost 1110 voters also gauged how people outside NSW believed Mr Morrison treated their state in comparison to his home turf.

Half of all Western Australian respondents believed the prime minister treated their state less favourably than NSW.

One in four Victorians felt the same while more than a third of Queenslanders thought NSW was receiving better treatment from Mr Morrison.

WA and Queensland were the bedrock of the coalition’s narrow election victory at the last federal poll.