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Labour trails the Conservatives in the polls but Mr Brown told activists in Coventry the test was "what you do in the difficult times".
And he urged them not to give Theresa May a "free hand" in Brexit talks.
Mr Brown, PM from 2007 to 2010, did not mention Labour leader Jeremy Corbyn during his 25-minute speech.
Instead he talked about individual Labour candidates acting as champions for industry, for families and for the NHS in the House of Commons.
Mr Brown attacked the Conservatives' record on the NHS and child poverty and argued that jobs, manufacturing and the car industry were at risk if Mrs May got "carte blanche to do exactly what she wants" in Brexit negotiations.
"Mrs May says she wants this single issue election to strengthen her hand with Europe. But... we don't know what her hand is - she is not telling us what her hand is in these negotiations."
He told an audience of Labour Party members that politics went in cycles: "You can be up in 1997 and down by the 2010s.
"You can be the darlings of the media, as Labour was for some time, and yet the very same media is now telling you, you're the enemies of the people. So yes, politics goes in cycles.
"The test, however, is what you do in the difficult times. It's that you don't lose the courage to fight for what you believe in, you don't stand back and say 'this is now not for me, it's too difficult', but you continue to fight and support and champion what really matters to the future of this country."
"It is our duty to show this country that there is a better way forward."
Mr Brown, who resigned as Labour leader after Labour lost power in 2010, stepped down as an MP at the 2015 general election.
His speech came as Labour dealt with the fallout from its draft manifesto being leaked, before it had been agreed by the shadow cabinet, the party's National Executive Committee and other Labour figures.
Conservative PM Theresa May has sought to play down talk of a landslide Conservative victory in the general election on 8 June, following major gains at the local elections last week.
She says she is fighting for every vote in order to strengthen her hands in Brexit talks and said in interviews on Saturday: "I will not take anything for granted and neither will the team I lead, because there is too much at stake."