"Much has been said over the last few days relating to our departure from Rangers Football Club," he said in a joint statement with assistant David Weir and head of recruitment Frank McParland issued through the League Managers' Association.
"At this stage, for legal reasons, it is inappropriate for us to comment in any great detail on our departure from the club.
"However, given that the club has seen fit to make detailed public statements, it is important that we should clarify certain matters and as such we would like to formally place on record, that at no stage did we resign from our positions at Rangers."
Rangers said under-20 coach Graeme Murty would take charge of the first team instead.
Wednesday's statement said Warburton, Weir and McParland were being advised by the LMA and expressed surprise that Rangers had yet to provide an explanation of why the club suggested the three had resigned.
The record 54-times Scottish champions are third in the standings, 27 points behind leaders and arch-rivals Celtic after returning to the top flight this season.
They were demoted to the fourth tier of Scottish football in 2012 after going into administration due to financial problems.
(Reporting by Alan Baldwin in London, editing by Ken Ferris)
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