The National Library of Wales advertised for a Welsh speaking boss despite a minister's objections.
The library had warned that appointing a non-Welsh speaking chief executive would be "open to public criticism".
But Lord Elis-Thomas was adamant there should be no such language requirement, according to emails seen by BBC Wales.
Welsh speaker Pedr ap Llwyd was appointed to the role in December. In a statement, ministers said they had wanted the widest field of candidates.
The emails, seen by BBC Wales' Newyddion 9 programme, show the level of the dispute between the library, based in Aberystwyth, and the Welsh Government.
Language campaigners Cymdeithas yr Iaith have accused Lord Elis-Thomas, deputy culture, tourism and sport minister, of acting "disgracefully".
In justifying the "Welsh essential" role, the library wrote to government officials saying: "90% of library staff are fluent Welsh speakers, who wish to live their everyday life speaking the language."
"If the library appoints a non-Welsh speaker, he/she will not be able to communicate with staff in their chosen language, and therefore will be working against the Welsh language measure 2010, bringing the library into disrepute and damaging the library's good name."
Outgoing chief executive Linda Thomas, who leaves the post next month, said resistance from the Welsh Government would be seen as "WG deliberately seeking conflict".
Discussing the matter over email with colleagues a government official said: "This gives us a real problem as the minister was equally adamant that it shouldn't be [Welsh essential] when I spoke to him a few days ago.
"I'm concerned that (on top of the broadcast archive issue) this could prompt a damaging public row".
Plans for the archive, to be based at the library, had been in doubt after ministers withdrew support - but the dispute has since been resolved.
In a subsequent email over the chief executive recruitment, Jason Thomas, who was representing the Welsh Government on the appointment panel, said: "Just to confirm in writing a conversation I just had with the minister on this.
"He reiterated his position and that this should not be advertised as Welsh essential.
"He wants to attract the broadest field possible."
Yet library president Rhodri Glyn Thomas decided to press ahead with the Welsh essential advert, a decision a government official described as a "serious development".
By the end of the process a government official said Lord Elis-Thomas was "not inclined" to challenge the library's decision but wanted to ensure the appointment was not a "borderline case".
Bethan Sayed, chair of the assembly's Culture, Welsh Language and Communications Committee, tweeted that she would ask the committee to formally write to the minister on the matter.
In a statement for Newyddion 9, the Welsh Government said its aim "was to ensure that the opportunity was there for the widest possible field of candidates and ensure that the best candidate was appointed to lead the library".