Senior party sources indicated last night that they were prepared to risk a "straight fight" between Mr Morgan and the new Welsh Secretary, Alun Michael, for the candidacy.
Although some will see the move as a huge political gamble, party officers claim they are confident that Mr Michael can win what is sure to be a divisive contest to succeed Ron Davies.
The chances of a direct run-off for the post became inevitable yesterday when the Cardiff West MP told the Welsh Labour Party executive that he was not prepared to step aside.
An emergency meeting of the executive in Cardiff yesterday decided to postpone making a decision on the party's means of choosing a leader. The executive, which was lobbied by noisy protests from members who fear Millbank will impose Mr Michael as sole candidate, will meet again later this week to make its final recommendations.
Mr Morgan agreed to talk to the meeting, but made clear that there was no chance of him taking up the offer of joining a "unity ticket" as Mr Michael's deputy. "I can tell you now there is more likelihood of Ian Paisley being the next Pope than of me agreeing to a fix or a stitch-up," he warned.
"An absolutely extraordinary level of support has been manifested to me in Wales."
More than 40 placard- carrying demonstrators chanted slogans outside the meeting, calling for the issue to be decided by a one-member, one-vote ballot of the 25,000 party members in the principality.
Mr Morgan, Mr Michael and Wayne David, an MEP who also aims to contest the leadership, had "constructive" round-table talks and will meet again later this week. However, the party leadership has now reluctantly accepted that a contest will go ahead, probably under the same electoral college that chose Mr Davies.
Mr Morgan's campaign was boosted last week when he topped an opinion poll as the public's choice for "Prime Minister of Wales" and was backed by a large majority of Assembly candidates. Yet Mr Michael's backers are understood to be confident that they can clinch the contest with the help of crucial votes of trade unions, co-ops and women's sections, MPs and MEPs. The full weight of the party machine will get behind Mr Michael and Mr David is likely to stand as his deputy to avoid splitting the Blairite vote.
Mr Michael attempted to win the party round yesterday with a raft of new proposals to increase the power of Welsh members over selection of their MPs and policy making. He said he wanted to overhaul MP selection and give Wales a representative on the party's ruling NEC.
Anita Gale, the general secretary of the Wales Labour Party, said there was no prospect of the contest being "stitched up by London".
Labour had the welcome distraction of the defection by Stuart Andrew, a Tory Welsh Assembly candidate who claimed that his own party was riven by disunity. The move is a setback for the Tories, who tomorrow will announce the result of their one-member, one-vote ballot of Welsh party members to choose their leader for the Assembly elections.
The contest is between a former Welsh Office minister, Rod Richards, and Professor Nick Bourne, the chief spokesman for the party in Wales.