The latest RedBridge/Accent Research poll and Newspoll for The Australian newspaper are among the first surveys since the fuel shortages began.
The RedBridge/Accent Research poll found in the preferred prime minister stakes Anthony Albanese sits at 33 per cent, down one point.
This could reflect some voter dissatisfaction with his management of the fuel pinch.
National cabinet will meet on Monday to discuss the Middle East fuel crunch for a second time.
State and territory leaders and business groups have called for a national approach to plot a path through the crisis as petrol prices surge and hundreds of service stations run dry.
The RedBridge/Accent Research poll of 1003 voters last week, found Labor's primary vote is steady at 32 per cent, while One Nation is the next most popular party with support going up a point to 29 per cent.
The Greens sit at 13 per cent, also up one point.
Despite new jockeys in the leadership saddles for the Liberal and National parties, the federal coalition is still in for a bumpy ride amid a One Nation surge.
The coalition's primary vote dropped two points down to 17 per cent.
Angus Taylor ousted Sussan Ley from the Liberal leadership in February while, Matt Canavan took the helm of the Nationals in March after David Littleproud's shock exit.
One Nation caused a major stir in the recent South Australian election.
The anti-immigration party beat the Liberals to come in second place with 22 per cent of the primary vote.
And while it might only translate to around four seats, analysts say One Nation should not be underestimated in other jurisdictions or nationally.
Meanwhile, the latest Newspoll had Labor's primary vote at 31 per cent and replicated the strong support for One Nation at 26 per cent ahead of the coalition on 21 per cent.
The poll had a sample of 1232 voters and was conducted last week.
Forty four per cent of voters surveyed said Mr Albanese is their preferred prime minister choice compared to 36 per cent support for Mr Taylor. The remainder were undecided.
The Labor leader's net approval rating has fallen further in this poll and sits at -18 per cent compared to Mr Taylor's -7 per cent.
Almost three quarters of those surveyed disapprove of the US war against Iran.
And 63 per cent oppose Australia sending naval vessels to assist the US in trying to keep the Strait of Hormuz open for shipping.
