The coalition has switched tactics on the carbon tax, accusing the Australian Greens of seeking a second wave of climate action, including an end to coal-fired power.
But the Greens say they have no plans to shut down the coal industry and will focus on selling the carbon pricing plan to the public.
Prime Minister Julia Gillard says coal, which currently produces about 80 per cent of electric power, will remain part of Australia's energy mix for at least another four decades.
A day after parliament passed the government's carbon pricing legislation, Nationals leader Warren Truss said Labor - which has taken a big hit in the polls since the laws were first announced eight months ago - should be concerned about the next phase.
"The Labor Party must be desperately concerned that their partners in government are not just satisfied with delivering to Australia the world's biggest carbon tax ... but now the Greens want to stop all coal-fired power stations," he said.
"The Greens will never be satisfied - they will want more.
"It's time the government cut the Greens loose and make it clear they will govern in the nation's interest."
Senator Brown said the issue of burning fossil fuels would be a debate for decades to come.
"I'm very happy to be involved in that debate," he told reporters in Canberra.
"If you are asking what next I'm going to do - I'm looking at getting out into the public arena and talking much more about what a win for Australia we saw in this parliament."
Asked if the Greens had a plan to end coal-fired power by 2050, he said: "No, we don't have one."
Ms Gillard, who was applauded for her climate action at a carbon expo in Melbourne on Wednesday, said while the carbon price would make coal-fired power more expensive, coal would continue to provide power for decades to come.
"We will still be using some coal in the middle of the century, but it will be a different energy mix than what we would have had in a business-as-usual case," she said.
The prime minister will discuss climate change in a number of forums during the next few weeks, including an Asia-Pacific Economic Co-operation (APEC) meeting and the East Asia Summit.
But she doesn't plan to raise it with US President Barack Obama during his visit to Australia next week.
"President Obama has announced an incredibly ambitious target for clean energy in his own market," she said, adding that individual US states were moving towards emissions trading.
Senator Brown said Australia would get "a lot of credit" for being a good global citizen in enacting its carbon pricing laws.
Ms Gillard predicted that if the coalition won the next election it would not repeal the carbon tax, despite its threats to do so.
"As the legislation comes into existence, the pricing starts, the investments start to flow, people get the tax cuts, the pension increases, the penny will well and truly drop that this is not something that can be undone or indeed that in truth they want to undo," she said.
Opposition climate spokesman Greg Hunt said the coalition remained determined to repeal the legislation.
"There would be an overwhelming mood in the community to repeal the tax," Mr Hunt said.
"The whole thing could be done and dusted within six months."
