Sir Keir Starmer has been warned against “watering down” the “radical policies” he promised during his campaign to become Labour leader.
The Fire Brigades Union told the BBC he must not “cede any ground” to the Conservatives and fight for “root-and-branch” reform of society.
General Secretary Matt Wrack added that he had not “heard Keir make that case” since becoming Labour leader in April.
Sir Keir has urged the party and unions to “stand together like never before”.
Labour’s four-day annual conference, the first under his leadership, began on Saturday.
Renamed Labour Connected, it is taking place online and will not feature votes, but the party’s major figures will still give speeches and take part in discussions.
In his campaign to become leader, Sir Keir set out 10 pledges.
Among these was putting a “Green New Deal at the heart of everything we do”, including a Clean Air Act to tackle pollution at a local level, and demanding “international action” on “climate rights”.
Sir Keir also pledged to work “shoulder-to-shoulder with trade unions to stand up for working people, tackle insecure work and low pay”.
He said a Labour government under him would repeal the Conservatives’ 2016 Trade Union Act, which makes industrial action more difficult.
Mr Wrack, whose FBU is one of the more left-leaning of the 12 Labour-affiliated trade unions, said: “Our present crisis has only made the case for that platform more urgent, but we haven’t yet heard Keir make that case in opposition.”
He said the Labour leader should promote the Socialist Green New Deal, agreed at last year’s party conference.
It calls for net-zero carbon emissions by 2030, bringing the energy sector into public ownership and the creation of hundreds of thousands of jobs in the environment sector, on union-negotiated rates of pay.
Mr Wrack said: “We look forward to seeing Keir making [the Socialist Green New deal] his own. But that can’t mean any watering down of the radical policies we fought for.
“We don’t want to see Labour cede any ground to the Tories, full stop – not least on the greatest issue of our time.”
Mr Wrack called Labour Connected “a chance for Keir and the shadow cabinet to prove to members that there will be no retreat on the policy pledges he was elected on”.
“Swapping to paper straws isn’t going to save our planet,” the FBU leader said. “Nothing short of a root-and-branch transformation of our society and economic system will save our planet from the brink of destruction.”
He added that rebuilding the economy after the pandemic “should be seen as an opportunity to tackle the climate crisis as well”.
The FBU split from Labour in 2004 following a dispute with Tony Blair’s government over pay. It re-affiliated in 2015 when Jeremy Corbyn became leader.
The union backed Rebecca Long-Bailey, another on the left of the party, against Sir Keir in the leadership contest earlier this year.
She was sacked from the shadow cabinet in June after she re-tweeted an article Sir Keir said “contained anti-Semitic conspiracy theories”.
In a separate development, Len McCluskey, leader of Unite, the UK’s second-biggest union, has promised to review its financial support for Labour.
Addressing the TUC Congress earlier this week, Sir Keir continued to promote a unifying message when he said: “Labour and the trade union movement need to stand together like never before, to show the British people that we’ve got their back and their future too.
“We’ll fight to protect jobs, incomes and working conditions at this time of national crisis, and show that there is a better, fairer society to come. That is our mission.”
Last week, TUC general secretary Frances O’Grady told the BBC that Sir Keir had made a “really strong start” as Labour leader.
The party has been contacted for a response to Mr Wrack’s comments.