The Senate has voted down legislation to axe the carbon tax - a core election promise of Prime Minister Tony Abbott.

After months of debate Labor and the Greens combined to vote against the repeal laws 33 votes to 29 today.

Labor, which introduced the carbon pricing scheme in 2012, says the Coalition's alternative policy to tackle climate change, called Direct Action, will be ineffective and too expensive.

"Without a credible alternative, Labor cannot support the abolition of the existing clean energy policies," Opposition climate change spokesman Mark Butler said.

Greens leader Christine Milne has issued a statement saying the current law, maintaining a price on carbon, must stand.

"The Senate has rejected Tony Abbott's do-nothing approach on global warming and voted to maintain the price on pollution," she said.

The carbon pricing scheme was brought in by the Gillard Labor government, after extensive negotiations with the Greens, and currently charges polluters about $25 per tonne of carbon emissions.

"Axing the tax" was Mr Abbott's catch-cry during last year's election campaign, and the Government says the Senate's move will cost jobs and hurt the economy.

Environment Minister Greg Hunt says the Government will take the laws back to the House to again try to have them passed.

"We would like the Parliament to respect the will of the people," he said a short time after the vote.

"And my hope and my belief is that if this Parliament will not do it, the new Senate in the first two weeks after July has given all the indications that they will respect the mandate given by the Australian people."

Earlier today, the Government had already reintroduced carbon tax-related legislation that could set the stage for a double dissolution election on the issue.

The Coalition wants to axe the multi-billion-dollar Clean Energy Finance Corporation (CEFC) but the Senate rejected the legislation in December.

Coalition Direct Action policy Keep the 5 per cent emission reduction target

Keep the 5 per cent emission reduction target Scrap the price on carbon and associated corporations

Scrap the price on carbon and associated corporations Establish a $2.55 billion fund to pay businesses for emission reduction projects

Establish a $2.55 billion fund to pay businesses for emission reduction projects Create a 15,000 strong Green Army to conduct conservation work Read more about the policy in our explainer Photo: AAP

The laws were brought back before Parliament this morning, and if voted down again would give the Government a trigger to call an election of both houses of Parliament.

Environment Minister Greg Hunt has criticised the Senate for staging a "go slow" on axing the price on carbon.

He says the Government will "push ahead" with a vote soon, including on the future of the CEFC.

"This is a $10 billion fund based on borrowed taxpayers' money," he said.

"It's an extraordinary borrowing against the will of the Australian people who voted to change the government.

"It's part of the repeal of the carbon tax package and we'll just keep going until it's done."

The corporation was set up by Labor to invest up to $10 billion in renewable energy projects and to help attract private sector investment.

Under the constitution, there needs to be a three-month gap between Senate votes on the same bill to give the government reason to call a double dissolution vote, which would involve the election of all 12 Senate positions from each state instead of the usual six.

Palmer's PUP to have crucial say in new Senate

But the Government may not force a vote before the Senate changeover on July 1, when the Greens lose the balance of power and Clive Palmer's PUP steps in to crucial Upper House seats.

The Palmer United Party has not yet made clear what its position is on repealing the carbon legislation, though Mr Palmer has criticised the tax.

He is also holding out on what the PUP senators - in coalition with Motoring Enthusiasts Party senator Ricky Muir - may do in relation to the Government's plan to repeal the mining tax.

Mr Palmer, whose businesses hold significant mining interests, has not paid the tax and has called for a tax amnesty.

However, this morning he told Radio National that he would not support the key Government measure if the Coalition went ahead with scrapping a welfare bonus attached to the tax.

Labor brought in the mining tax with boosts to welfare payments including a $200 annual bonus to the children of Defence personnel who are killed in service.

Mr Palmer said the Government was attacking "defenceless children".

"We don't support the repeal of the mining tax taking $250,000 off 1,200 orphans of serving veterans, and we think if a person's given their life for Australia they should be sure that the Australian Government won't attack their children after they're gone," Mr Palmer said.

But the Coalition says the tax needs to be scrapped and so do any associated benefits.

And Veterans' Affairs Minister Michael Ronaldson is standing by the plan.

"Of course I'm happy to talk to Clive about it, but can I just make it clear the Government has made no changes whatsoever to the two education programs that support the children of veterans and orphans," he said.