Mr Meacher's declaration means that Mr Brown will not have a clear run in the final stage of his long political journey to replace Tony Blair, who is expected to announce a timetable for his resignation as prime minister and leader of the Labour party next week.
Speaking following the routing Labour received in Thursday's local and devolved elections across England, Wales and Scotland, Mr Meacher said: "I am intending to stand. I don't agree that the party doesn't have the stomach for a fight."
The MP for Oldham West and Royton said that Labour had suffered a "pretty serious setback" last week, when the Scottish National Party (SNP) seized power from the UK's governing party north of the border and almost 500 council seats were lost by Mr Blair's foot soldiers.
Calling for a "change of direction" Mr Meacher said that New Labour had "run its course" and told Reuters that his party needed to reengage with voters who had lost faith in it over the Iraq war and a failure to deliver successful public sector reforms.
Mr Meacher, who declared his intention to fight for the Labour leadership in February, last week agreed with his potential left-wing rival John McDonnell that whichever of them received the least nominations from the party's MPs once a contest was declared would withdraw to give the other a better chance.
But while such a move could harm Mr Brown's campaign, the chancellor's chances of entering Downing Street received a boost today after the prime minister directly endorsed his ability to lead the country for the first time.
Writing in the News of the World, Mr Blair admitted that Labour would have a tough fight to secure a fourth consecutive term in office at the next election, but argued that the policies of David Cameron's Conservative party were "not thought through."
"Gordon Brown by contrast is completely thought through," he added, praising the chancellor's stewardship of the economy.
Mr Brown's hopes of becoming the next Labour leader are now expected to be further helped by an anticipated statement from home secretary John Reid who, according to reports, will say that he will not challenge him for the role.
Environment secretary David Miliband last month quashed speculation that he would fight to replace Mr Blair, telling the Observer newspaper that he would back Mr Brown in a leadership contest.
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