Independent senator David Pocock has agreed to back the Albanese government’s pivotal climate bill – but has flagged he might sink future efforts, unless Labor sets more ambitious targets on global warming.

In the first major test of the federal government’s relationship with the upper house crossbench, Senator Pocock said on Tuesday he would vote in support of Labor’s bill to create a legally-binding national target to cut greenhouse emissions by 43 per cent by 2030.

It came after the government agreed to support what Senator Pocock described as “sensible” amendments.

His support is crucial to securing the bill’s passage through the upper house, with the Greens also set to back it.

The Senate is expected to vote on the legislation this week – likely on Wednesday – after debate resumed in the upper house on Tuesday afternoon.

“We’ve been having some good productive discussions with (Climate Change and Energy Minister) Chris Bowen and his office,” Senator Pocock said on Tuesday.

“The amendments we’ve been putting forward I believe are really sensible and they add to the transparency and accountability of the bill.”

The bill is one of the Albanese government’s first pieces of legislation. Labor has already agreed to amendments pushed by independent MPs in the lower house in July.

After meetings with Senator Pocock on Monday, Mr Bowen said the government had agreed to further amend its bill to include provisions about how climate risks were reported.

It had also agreed to tighten rules about how the Climate Change Authority provided advice and when that advice should be tabled in parliament.

“That’s what we would intend to do, but [we’re] happy to enshrine it in legislation going forward,” Mr Bowen told Sky News on Tuesday.

“[Senator Pocock] had a range of constructive suggestions [and] we don’t agree about everything. There’ll be a couple of things that he moves that we won’t support, but we are more than happy to support his very constructive suggestions.”

Among the rejected amendments were a push from Senator Pocock and Tasmanian crossbenchers Jacqui Lambie and Tammy Tyrrell to require the government to report on expected greenhouse gas emissions from budget spending.

The senators also want the government to scrap two controversial elements of the Emissions Reduction Fund, which pays businesses for the carbon sequestered by projects they invest in.

“The Jacqui Lambie Network and I worked on some measures around the budget and actually looking at greenhouse gas emissions for new projects or big spending lines over the forward estimates. That’s not something the government wants to do,” Senator Pocock said.

“Myself and the Jacqui Lambie MPs feel like that would be a pretty big measure in terms of transparency and accountability in terms of how we’re actually spending the money.

“That’s not where the government wants to go.”

The New Daily contacted Senator Lambie’s office for comment.

Ahead of the election, Senator Pocock campaigned on stronger action on climate change and his vote could be a deciding factor on other Labor plans to rewrite environmental protection laws and review the carbon credits scheme.

Asked if he was prepared to vote against future Labor climate bills, Senator Pocock said: “As an independent, I’m not here to rubber-stamp”.

“When it comes to the EPBC (Environment Protection and Biodiversity Conservation) Act, our environmental laws in Australia … they no longer work,” he said.

“It’s going to have to be a fundamental shift in the way that we enact environmental law.

“It is ultimately about compromise and finding something that will work but we have to get it right and we have to be more ambitious.”

The Greens have already indicated they will support the climate change bill, despite stating they believe Labor’s 43 per cent reduction target is inadequate.

On Monday, the Greens introduced a “climate trigger” bill that seeks to stop approval of new coal and gas mines.