The Senate could vote on the coalition’s carbon tax repeal bill before Christmas, after Labor and the Australian Greens stymied each other’s attempts to establish separate parliamentary inquiries.

The Greens voted down a Labor motion to set up a Senate inquiry into the legislation, while Labor helped defeat the minor party’s move for an inquiry into the government’s direct action policy.

Greens leader Christine Milne said her party did not want to avoid a vote on the repeal bill.

“It is time to take it straight up to the coalition government,” she told parliament.

The government introduced the repeal bill to parliament on Wednesday.

It is expected to reach the Senate in early December in time for the final fortnight sittings of the year.

Labor’s senate leader Penny Wong told parliament it was “frankly ridiculous, inappropriate and undemocratic” for the Senate to be asked to vote on the repeal legislation before the government was transparent about its direct action measures.