 Peter Hain also hopes to become Labour Party deputy leader |
The Conservatives and Plaid Cymru say a top judge's criticism of Peter Hain raises questions about his role. Mr Justice Girvan called for an inquiry and said the Northern Ireland interim victims' commissioner's appointment was "motivated by improper purpose".
Conservative Wales frontbench spokesman David Jones urged the Wales and Northern Ireland secretary to consider whether he could carry on in the posts.
Mr Hain said he was "studying the judgement carefully".
The High Court judge upheld a judicial review application challenging the appointment of Bertha McDougall as Northern Ireland's interim victim's commissioner - a post to champion the interests of victims of the Troubles.
 | The comments are scathing, as trenchant as you can get from a High Court judge |
The judge said the appointment of Mrs McDougall, whose policeman husband was murdered by the republican INLA, was a politically motivated confidence-building gesture to unionists.
He said Mr Hain failed to consider that there was no evidence that Mrs McDougall would command support from both nationalist and unionist communities.
Mr Justice Girvan also accused civil servants of "providing misleading and incorrect information" about the appointment process.
He said "This case raises very serious issues which should be the subject of immediate and searching enquiry at a high level".
Tory Clwyd West MP Mr Jones described the judge's comments as "trenchant, very damning criticism".
He said sensitive negotiations to establish a Northern Ireland Executive made this a very difficult time for Mr Hain.
Mr Jones said: "It's a very very demanding call for anybody to do two important jobs as secretaries of state and I think he ought to give serious consideration as to whether he can carry on doing both".
'Big picture'
Mr Llwyd, a barrister, told BBC Wales' Dragon's Eye programme that the judge's criticisms were "devastating".
"The comments are scathing, as trenchant as you can get from a High Court judge," he said.
He added: "If the judge's criticism is well founded... then it calls into question the confidence of the people of Wales in the secretary of state and secondly whether (he) in due course should consider his position".
A spokesman for the secretary of state said Mr Llwyd's comments were "preposterous".
Mr Hain told BBC Wales he was considering the judge's criticisms but stressed the importance of the work being done on the ground in Northern Ireland.
He said: "Obviously, we're studying the judgement carefully and we're looking at the consequences of that.
"But the big picture is I was acting on behalf of victims and will continue to do so."
Dragon's Eye is on BBC 2W at 2100 GMT on Thursday, and on BBC One Wales at 2240 GMT.