It was the second session this week that the 62-times capped Llanelli Scarlets outside half had successfully completed and his progress has thrilled the Welsh coaching team.
"Stephen has come through a couple of training sessions now and is 100 per cent fit," declared Davies. "That is great news for the squad.
"No firm decision has been made on whether or not he will figure at the weekend. Our only other outstanding injury now is with lock Ian Evans, who is hoping to be in the mix for the Australian game in Cardiff next week."
Jones damaged his groin in the practice match that rounded off Wales's training week in France in July on the same St Nazaire pitch he successfully trained on yesterday, and there were fears he might not be fit for selection for the opening Pool B clash with the Cannucks this weekend.
Even Jones himself, who is preparing to play in his third Rugby World Cup, was a worried man.
"I have to admit there was a time when I thought I might have to miss out on the World Cup," admitted Jones, who was absent throughout Wales's three warm-up matches against England, Argentina and France in August.
"It wasn't until I got back home and the Welsh doctors scanned the injury and gave me the results that I knew I could make it. I am deliriously happy to be back in full training and to be in France with the squad.
"It was nice to be able to come through a full session on the pitch where I picked up the injury and now it is all systems go.
"I've been confined to the gym for the last couple of weeks and so it was good to get some sun on my back. We've had a fantastic reception from everyone in France and I can't wait to get back into a competitive game situation."
More than 1,000 locals turned out to watch Wales's first training session at St Nazaire rugby club and the players warmed to their support.
"It was amazing to see 1,000+ fans at our training session today and that left us in good spirits. We've had a wonderful reception from the locals and it was so easy to settle into our apartments having been in Pinochet for our training camp in July," said 72-times capped back rower Martyn Williams.
"We really are in wonderful surroundings and it is great to be back here and finally getting ready for the World Cup. It's good to finally be in tournament mode and getting ready for the real business of the year after our warm-up matches.
"There will be nothing else for us to focus on other than the World Cup over the next six weeks. We have a tough opening game against the Canadians in Nantes on Sunday and we know just how hard it is going to be for us in that game.
"They have a lot of experience and we know a lot of their players. But all our conditioning and weight training is now over and we are looking forward to really getting into rugby mode; everything we have been doing has been geared towards us reaching a rugby peak from Sunday onwards."