The backbench MPs opposed to the Safe Schools Coalition must drop their attack on the program following the Government's review and move on, say the Greens.

"This review was pointless to begin with and now we've got coalition MPs throwing a tantrum because they don't like the outcome. They need to put the safety and well-being of LGBTI young people ahead of their political ideology and stop their homophobic crusade against Safe Schools," Greens sexuality spokesperson Senator Robert Simms said.

The Australian Greens have secured time on Thursday to debate the Greens' Marriage Equality Amendment Bill and are calling on the Government, ALP and crossbenchers to vote in favour of the reform.

"The Greens have secured an opportunity to bring on a vote in the senate for marriage equality this Thursday during private senator's time," Greens marriage equality spokesperson Senator Robert Simms said.

"Today we've seen misleading and outrageous claims from Labor that the Greens voted against our own same-sex marriage bill. This is simply untrue.

The Australian Greens will be moving to bring the issue of marriage equality to a vote in the Senate on Thursday.

"This matter has been debated in the community and the parliament for years, it's time for a vote," Greens marriage equality spokesperson Senator Robert Simms said.

"The Labor party has private senators' time available on Thursday and we will be moving to use this time to debate and vote on the Greens' marriage equality bill.

The Australian Greens say Malcolm Turnbull should dump his plan for a plebiscite on marriage equality, following new research that shows it will cost the economy more than half a billion dollars.

"Today's PwC report should really be the nail in the coffin of this plebiscite plan. How can a prime minister who promised to get our national economy back on track proceed with such a flagrant waste of tax payer money?" Greens marriage equality spokesperson Senator Robert Simms said.

The Australian Greens are calling on the Government to dump the marriage equality plebiscite and bring on a free vote in the parliament.

"The confusion continues today with Prime Minister Malcolm Turnbull and Attorney General George Brandis appearing to take different positions on the plebiscite timeline," Greens marriage equality spokesperson Senator Robert Simms said.

"The plebiscite plan has completely unraveled over the past few months.

The Australian Greens have called on the Federal Government to fast-track the approval of HIV-prevention medication, Pre-exposure Prophylaxis (PrEP), following Canada approving it.

Canada joined the United States and France in approving Truvada late last month.

"The approval of PrEP drugs should be fast-tracked by the Australian Government," said the Greens' spokesperson on Sexuality, Senator Robert Simms.

The Australian Greens will tonight table two petitions - one from the Greens and one from international LGBTIQ advocacy group All Out - totaling more 70,000 signatures supporting Safe Schools. The petitions were launched in response to Senator Cory Bernardi's petition of 9499 that lead to the Prime Minister calling for an investigation into the program.

This edition of Simms in the Senate covers the Greens' campaign to make schools safe for LGBTI students, why there should be no nuclear waste dump in South Australia, the inquiry into BP's exploration of the Great Australian Bight, green cars being key to SA's economic future, a Valentine's Day push for marriage equality legislation,

The Australian Greens have warned a homophobic pamphlet distributed by former a Liberal MP is a window into the campaign being planned by opponents of marriage equality, in preparation for a plebiscite on the issue.

"During the last week we have seen a tsunami of vile homophobia fanned by people like Cory Bernardi and George Christensen. This flyer is the latest example of this ugly campaign against equality," Greens marriage equality and sexuality spokesperson Senator Robert Simms said.