The Commonwealth countries are high on the UK’s list of potential free trade partners post-Brexit but Mr Juncker suggested the EU should try to muscle in first.
In his annual State of the Union speech at the European Parliament, Mr Juncker said he would seek to initiate free trade talks with Australia and New Zealand.
And he said he would like to see them completed by 2019 – just as Britain becomes free to launch free trade talks of its own.
Mr Juncker said: “Today, we are asking that we open up negotiations with Australia and with New Zealand.
“I am asking that we complete these negotiations by the end of our mandate in late 2019.
“We are not naive free traders. Europe will defend its strategic interests with an EU framework for investment screening.
He said “the wind is back in Europe’s sails” after the shock of Brexit and insisted the continent was unifying as economic momentum gathered pace.
He said: ”We have now a window of opportunity but it will not stay open forever.
“Let us make the most of the momentum, catch the wind in our sails.”
Mr Juncker also said he would seek powers to screen foreign takeovers in Europe’s strategic sectors amid worry about investment by China.