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.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.