"He emphasised the importance of setting ambitious targets to cut emissions and reach net zero," the Downing Street spokesperson said.
"The Prime Minister also stressed that we need bold action to address climate change."
The United Kingdom has set a goal of reaching net zero emissions by 2050 but Australia has resisted adopting similar measures.
A spokesperson for Mr Morrison adopted a different tone in their summary of the phone call between the two leaders - with no mention of reaching net zero emissions.
"Both countries agreed to work closely together to accelerate research and deployment of low emission technologies," the spokesperson for Mr Morrison said.
Labor's foreign affairs spokesperson Penny Wong seized on the differences between the two documents in a Senate estimates hearing on Wednesday.
"One mentions net zero! One doesn't! It just ignores it!" Senator Wong asked Foreign Affairs Minister Marise Payne.
"Your government is increasingly isolated globally on climate change."
"I absolutely dispute that Senator - this government has made it crystal clear that we are absolutely committed to the Paris agreement ... we are taking real and practical action," Senator Payne responded.
Senator Payne said this included progressing the nation towards net zero emissions in the second half of the century.
The pair also discussed a free trade deal and their response to the coronavirus crisis before the British leader shifted the conversation to climate change.
Mr Morrison has previously said it is "absolutely achievable" for Australia to drive down emissions to net-zero.
The prime minister told reporters on Wednesday Australia and the United Kingdom continued to transform their economies to lower emissions.
"One thing the British Prime Minister and I agree on is that achieving emissions reductions shouldn't come at the cost of jobs in Australia or the UK," he said.
Japan - the world’s fifth-biggest emitter of carbon dioxide - this week committed to a net-zero emissions goal by 2050. China has also committed to reaching net-zero emissions by 2060.
Labor, business groups and the National Farmers Federation have urged the federal government to also adopt a target of net zero emissions by 2050.
Additional reporting by AAP