Rhodri Morgan was welcomed to the conference platform by the Prime Minister
Rhodri Morgan says he will announce his departure soon as Welsh Labour leader and first minister.
But while he told the party it was his last speech to the annual conference in the job, he gave no details about what he called "Wales' worst-kept secret".
He had previously said he would reveal when he is going on or around his 70th birthday, which is on Tuesday.
However, watched in Brighton by Prime Minister Gordon Brown, he said his leadership "does not have long to run".
Instead, he told party members that he will give further details "before too long" about his departure.
Mr Morgan is understood to have been reluctant to reveal his plans to a gathering in England.
We have temporarily mislaid that magic recipe for blending the mushy peas of old Labour with the guacamole of New Labour... we will find that recipe again soon
First Minister Rhodri Morgan bids farewell to the conference
BBC Wales political correspondents reported that Mr Morgan had considered making the official announcement to this conference, and as late as Sunday morning colleagues said he had had yet to decide the timing of his statement.
Acknowledging the difficulties facing Labour, Mr Morgan said the party had to rebuild the coalition which swept it to power in 1997.
"I know that we are in difficulty now. We have temporarily mislaid that magic recipe for blending the mushy peas of old Labour with the guacamole of New Labour.
"Those difficulties will be temporary. We will find that recipe again soon.
"Because when the country is in difficulties, the government always takes a hit - it always happens.
"But when a country is in difficulties, that is precisely when you need the intervention of a Government that actually believes in intervention. That means Labour."
Rhodri Morgan on 'Wales' worst-kept secret'
He told the conference: "While my Labour leadership in Wales may not have long to run now, Labour's role of leadership in Wales and in Britain certainly is not coming to an end any time soon".
He thanked Labour for having come with him on his journey to establish Wales as a "yes we can country".
He said the decade since devolution had been the most "important thing to happen since the industrial revolution" for Wales.
He was given a standing ovation by activists, led by the prime minister.
Meanwhile, Welsh Secretary Peter Hain, who also spoke to the conference, has said he is not backing any of the three likely candidates to succeed Mr Morgan as Welsh Labour leader and first minister.
Speaking to the Politics Show Wales, he said Counsel General Carwyn Jones, Health Minister Edwina Hart and Merthyr Tydfil and Rhymney Assembly Member Huw Lewis were all "high quality candidates" who would be "well up to doing the job of first minister".
Mr Hain said that when Mr Morgan did leave he would be "a big loss to Welsh Labour and to Wales".
"And all of the high quality candidates who have indicated that they are wanting to replace him will have to prove themselves in a succession election.
"I'm not backing anybody. As secretary of state for Wales I am staying entirely neutral on this, as you'd expect."
Mr Hain has also warned that Labour faced a "really bad defeat" at the next general election unless it raised its game.
He suggested the government had made a number of mistakes in recent months and must "collectively do much better".
"There have been too many instances where we haven't done as well as we should have done - the 10p tax, the Gurkhas, Lockerbie," he told The Sunday Times.
He also admitted that the row over the release of Lockerbie bomber Abdelbaset Ali Mohmed Al Megrahi was not the government's "finest hour".
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