First Minister Rhodri Morgan has urged the chief executive of the Welsh Development Agency to reconsider his resignation.
Graham Hawker had been at the WDA since November 2000
Graham Hawker stepped down from his post on Thursday following the Welsh Assembly Government's decision to abolish three major quangos.
But, speaking on BBC Wales' Dragon's Eye programme Mr Morgan said it was better to have strong leadership during a transitional period.
The first minister will meet staff from the WDA, Wales Tourist Board and post-16 education body Elwa on Friday.
On Wednesday he announced that the three would be taken over by his government by June 2006, with more quangos likely to follow
Mr Morgan said it was extremely improbable, though not impossible, that others would follow Mr Hawker's lead - and asked him to change his mind.
"I can't stop him from resigning," Mr Morgan told Dragon's Eye.
"I understand that it's a little bit equivocal what he's said but I've not seen it myself.
"Obviously that's between him and the board. We don't appoint chief executives of quangos."
Mr Hawker, former chief executive of utilities company Hyder, told his staff on Thursday that he was ill-equipped to lead the WDA - Wales' main economic development body - into the civil service.
Mr Hawker announced his decision to resign at the assembly's economic development and transport committee on Thursday afternoon.
In a statement to WDA staff, he added: "I explained (to the committee) that while the decision to abolish the WDA was a matter for the democratically-elected Welsh Assembly Government, I do not believe that I am well placed to lead the organisation into the civil service.
"In leading change, any leader has to display enthusiasm for that change.
The Welsh Assembly Government will control the three quangos
"I believe that I am ill-equipped to lead the WDA into a civil service organisation.
"I therefore intend to stand down."
Mr Hawker later told BBC Wales: "I think it's a cultural issue.
"We have a certain culture in the WDA - there's a different one in the civil service.
"The WDA is a very commercial organisation and that's going to be a hard match with a civil service culture."
Following the resignation, WDA chairman Roger Jones told BBC Wales he had known nothing of Mr Hawker's intention to step down.
Mr Jones paid tribute to Mr Hawker, adding that he would be missed on the WDA's board.
The WDA is the biggest employer of the three, with more than 900 staff. Elwa has almost 500 workers, and the tourist board more than 100.
Jeff Evans, of the Public and Commercial Services union (PCS), said it was bound to be a worrying and unsettling period for staff and that trade unions now needed clarification on the implications.