Voters likely headed for July 2 election

The prime minister expects the election to be on July 2 and will ask the governor general to dissolve both houses of parliament after the budget.

Prime Minister Malcolm Turnbull (L) and Leader of the Opposition Bill Shorten arrive during the reopening of Parliament in the Senate chamber. (AAP) Source: AAP

Prime Minister Malcolm Turnbull will wait until after the May 3 budget to ask the governor-general to dissolve both houses of parliament and call a July 2 election.

Mr Turnbull declined to be more specific about when he would make an election announcement, preferring to say it would be at an "appropriate time" after the budget.

The prime minister has until May 11 to make the call.

The federal government was handed the trigger for a double-dissolution election on Monday night after the Senate once again rejected legislation to restore the Australian Building and Construction Commission.

The bills were defeated 36-34, with crossbenchers Jacqui Lambie, Glenn Lazarus, Ricky Muir and John Madigan siding with Labor and the Greens.

Mr Turnbull has vowed to use a second rejection of the bills as a trigger for a July 2 election, insisting the construction industry needs a cop on the beat to stamp out misconduct following last year's damning royal commission report into union corruption.

MPs and senators were recalled to Canberra on Monday by Governor-General Peter Cosgrove at Mr Turnbull's request, in a constitutional move not used for 40 years, to consider the industrial reform bills.

Independent senators Madigan, Lazarus and Lambie ruled out support, insisting they weren't afraid of an early election.

Motoring Enthusiast Senator Muir said he didn't see much point continuing the debate given the government's unwillingness to consider his proposed amendments.

"If the government won't even consider what I believe to be reasonable amendments at least worthy of debate in this chamber then let's get this bill as it's presented to a vote.

"Then the government can proceed with what it wants, an early election."

Labor accused Mr Turnbull of misleading the governor-general over his reasons for proroguing parliament, using "propaganda" to justify restoring the ABCC.

Mr Turnbull's claim the ABCC would lead to improved productivity was a "complete untruth", based on discredited reports and figures from "cash for comment" consultancy firms, senior Labor senator Doug Cameron said.

"The prime minister misled the governor-general and he knows it."

The bills robbed construction workers of basic human rights and put their lives in danger, he said, with evidence showing a rise in workplace deaths when the commission was established by the Howard government.

The Senate has also been asked to reconsider the government's registered organisations bill, which is already an early election trigger having been rejected several times.

The government also wants the Senate to consider legislation abolishing the Road Safety Remuneration Tribunal.