The backbench Labour MP fired the first shots in what could be a bitter and hard-fought battle against Downing Street's preferred choice, Alun Michael, the Secretary of State for Wales.
Mr Morgan, currently clear favourite in the opinion polls, said his leadership bid would be based on breaking down barriers and keeping the assembly free of party machine politics and "jobs for the boys".
Mr Michael has strenuously denied suggestions that he has been "parachuted in" by 10 Downing Street to be successor to Ron Davies, who last month resigned from the Cabinet and the Welsh leadership after the incident on Clapham Common.
"The assembly belongs to the people, not to the Welsh establishment. Our assembly must be sleaze-free, right from day one," Mr Morgan told a Cardiff news conference.
"May 7 1999 is the day on which Wales stops being administered as a government department and starts being run as a country. That must mean few, if any, quangos; no vested interests and no narrow sectionalism."
Among those publicly backing Mr Morgan was miners' leader Tyrone O'Sullivan, chairman of the workforce who successfully re-opened Tower Colliery after buying it from British Coal. "I believe Rhodri is now the natural leader of Wales. Wales is a radical country and we need radical politics," he said.Reuse content