In a blow for the government, Labor and the Greens teamed up to tie an upper house vote, effectively stripping out the third and final stage of the cuts due to start in 2024.

But the government can restore the package to its original form in the House of Representatives where it controls the numbers, before bouncing the bill back to the Senate for approval a second time.

Prime Minister Malcolm Turnbull told reporters "of course" the government will send the bill back to the Senate, because the coalition is committed to the full tax plan.

Labor also opposes stage two of the plan, which includes increasing the top threshold for the 32.5 per cent tax bracket from $90,000 to $120,000.

Finance Minister Mathias Cormann said Labor had effectively endorsed the second stage by only asking the upper house to vote on cuts starting in 2024.

"Somewhere overnight the Labor Party position has shifted," Senator Cormann told parliament on Wednesday.

"It makes absolutely no sense for you not to have tried to get your policy tested in the Senate. You did not even try."

There is broad support for the first tranche of tax cuts, which introduce a new low- and middle-income tax offset worth up to $530 for individuals from July 1.

But Labor is trying to strip away the remaining parts of the package.

When the tax cut debate resumes, the opposition has another amendment to dump the second stage of the package from the legislation.

Australian Associated Press