RFU council member Alex Murphy tabled the motion against Thomas and it was defeated comfortably, a source close to the meeting told Press Association Sport.
Thomas, who took on the role of chief executive following Sir John Steele's departure in June, stood down as chairman in July and has been under fire for most of the summer.
Thomas has been heavily criticised by Judge Jeff Blackett in his report into the departure of predecessor Steele.
A decision was taken earlier on Friday to release Blackett's report.
The RFU council also moved to appoint Paul Murphy as chairman. Murphy took on the role of interim chairman after Thomas left in July and will not assume the post on a permanent basis before next summer's AGM, when there will be an election for the post.
Murphy, speaking outside Twickenham after his appointment, gave no indication whether he would look to stand for election at that meeting, which will take place in July 2012.
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