The two party leaders have still to agree on their cabinet

The leaders of Welsh Labour and Plaid Cymru had been due to meet last week to shape the new assembly government.

But it was postponed when Mr Morgan, 67, was taken to hospital, where he had artery surgery.

They are expected to decide who will be in the new Labour-Plaid Cymru coalition cabinet.

There is speculation that Plaid will have at least three ministerial posts.

But even if Mr Morgan and Mr Jones agree a new cabinet, there may not be an immediate announcement as nominees must be approved by the Queen.

The parties, who have traditionally been bitter enemies, had agreed a groundbreaking coalition deal on 6 and 7 July.

But within hours, Mr Morgan had to undergo a surgical procedure at the University Hospital of Wales in Cardiff.

Face-to-face

Although the final look of the new assembly government has yet to be decided, the Plaid leader has, in the meantime, been confirmed as deputy first minister, a role which was set out in the agreement between the two parties.

Tuesday's meeting in Cardiff Bay was their first face-to-face since Mr Jones took the first national government post in Plaid's 82-year history last Wednesday.

The day after, the Plaid leader immediately left for Belgium to represent Mr Morgan at the 90th anniversary commemoration of the World War I battle of Passchendaele.

On Monday, Mr Jones also represented the Welsh Assembly Government at the British-Irish Council in Belfast.

That conference was the first time Prime Minister Gordon Brown met the new leaders of the UK's devolved governments since he took on his new job.