“The Greens have improved a weak climate bill and we will pass it," Bandt told the National Press Club.
"But the fight to stop Labor’s new coal and gas mines continues and, in this Parliament, the only obstacle to stronger climate action is Labor,” Bandt added.
With the Greens’ backing, the bill only needs the support of one of the six remaining unaligned senators to achieve a majority in the 76-seat chamber.
Albanese did not say which senator or senators had promised support or what his government had conceded. But he said senators outside government did not get a “whole lot of things that they want.”
“We made our position very clear. There will be some amendments passed in the House of Representatives that are sensible, that are consistent with our position,” Albanese said.
Labor has a narrow majority in the House of Representatives.
Climate Change Minister Chris Bowen said a legally enforced target would instill confidence in business to invest in clean energy.
“It’s now very clear that our legislation will pass the Parliament,” Bowen said.
The conservative coalition that ruled for nine years until the election won’t budge from its 2015 Paris commitment to reduce emissions by between 26% and 28%.
When Labor was last in power between 2007 and 2013, its climate plans were rejected as too ambitious by the conservatives and not ambitious enough by the Greens.
Environmentalists criticized the Greens for rejecting a Labor bill in 2009 that would have made polluters pay for their greenhouse gas emissions through an emissions trading scheme because the Greens wanted deeper reductions.
Labor and the Greens agreed on legislation that imposed a carbon tax on 350 of Australia’s biggest polluters from 2012, but a conservative government removed the tax two years later.