Australian officials including Trade Minister Don Farrell met with a delegation of the EU Parliament Committee on International Trade (INTA) at Parliament House in Canberra on Monday to discuss its progression.
Negotiations with the bloc stalled under the former Morrison government over Australia's perceived lack of action on climate change, and the souring relationship with Paris after the dumping of a $90bn contract for French submarines.
The EU has welcomed the Albanese government's pledge to cut emissions by 43 per cent on 2005 levels by 2030, and Australia's strong military support for Ukraine following Russia's invasion.
INTA committee chair Bernd Lange said the last time the entire delegation had travelled to Australia was the launch of negotiations in 2017, and he wanted this to be the "eve" of the conclusion of the deal.
He said he wanted the trade deal ratified by the end of the EU parliament's term in 2024.
Senator Farrell, who was greeted by the EU ambassador-designate to Australia Gabriele Visentin, said discussions were "behind the eight ball".
"We're prepared to make all the time available that we need to achieve an agreement," he told the delegation.
"We want it to be a long and lasting agreement that benefits the people of both countries, expresses our democratic values and improves on the prosperity."
Senator Farrell said officials also discussed sustainable development during the meeting, and how Australia could become a leading global supplier of green energy.
He said Australia wanted to "build on the democratic ties" it held with Europe, noting during Prime Minister Anthony Albanese's first Europe trip he visited Ukraine in solidarity.
The European market has a gross domestic product of about $23 trillion, and Australia is seeking to improve access for agricultural and industrial products as well as create new opportunities for education, financial and professional services.
Meanwhile, a public hearing into the free trade agreement between Australia and the United Kingdom will be held by a parliamentary committee on Tuesday.