Australian voters have given Prime Minister Scott Morrison a cautious boost in his first days in the job, ranking him ahead of Opposition Leader Bill Shorten in key electorates even as his government trails Labor in the polls.

Voters have turned on the government in crucial marginal seats in NSW and Victoria but have kept their support steady in the vital Queensland electorate of Dickson, suggesting failed leadership challenger Peter Dutton may keep his position in Parliament.

A convincing majority of Australians want Mr Morrison to make sure his government runs its full term, warning against a rush to the polls after the chaotic removal of Malcolm Turnbull last Friday.

Prime Minister Scott Morrison at Parliament House over the weekend. Credit:Alex Ellinghausen

Voters have also panned the Liberal Party decision to dump Mr Turnbull and made it clear they do not want the new Prime Minister to withdraw from the Paris agreement to cut greenhouse gas emissions.