Trade Minister Don Farrell walked away from the bloc's previous offer following rounds of negotiations because it failed to give Australian agricultural products greater market access, which remains the sticking point.
Senator Farrell met face-to-face with the EU's trade commissioner Maros Sefcovic for the first time on Wednesday, on the sidelines of an OECD meeting in Paris.
Prime Minister Anthony Albanese said there was bipartisan support for free and fair trade.
"We will seek a deal that is good enough for Australia," he told reporters on Thursday.
"If it benefits us, we'll be in it. If it doesn't, we'll continue to not sign up to something that is not in our national interest."
Mr Albanese said Australia's free trade agreement with the UK had led to an increase in meat exports, in addition to wine.
"Why is that the case? Because our products are damn fine and they are in demand right around the world," he said.
Talks for a deal with the EU began in 2018, and that involves consulting all 27 member states before an agreement can be sealed.
There are more than 450 million consumers in Europe.
Countries across the world seek to diversity trade in the face of the US president's tariffs, with levies on steel and aluminium since doubling to 50 per cent.
Australian products are subject to a 10 per cent baseline tariff.
The trade minister said an agreement with the bloc would build resilience in a rapidly changing global environment.
"Both Australia and the EU recognise that now is the time to strengthen our economic partnership, and we're working through the remaining issues to try and finalise the deal," he said.
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