The family stated: "His fighting spirit is self evident as he has had a number of issues that he's overcome. Keagan's family would like to thank all who've sent their best wishes and to the wider cycling community who have sent literally thousands of positive messages."
Desere said that her son was "in recovery and still critical" after surgery, and had lost a lot of blood. She had earlier told a South African news site that "he's fighting for his life right now - we're waiting for another update this morning".
The family had to endure initial reports that Keagan had died form the accident, which occurred on the final stage as Girdlestone was getting back into the race after an earlier crash. The race was immediately cancelled.
"We just had to believe it wasn't true and and wait for official news," said Desere Girdlestone.
"Whoever started the rumour or thought it was their place to post it is beyond my comprehension.
British cycling star Chris Froome is among those to have sent messages of support. The double Tour de France winner posted: "Keep fighting" and expressed relief that initial reports that Girdlestone had died were false. New Zealand cyclist Greg Henderson tweeted: "Good luck Keagan. Focus on the positive."
Another British star Mark Cavendish tweeted:"Fight for you Keagan!!! @Keagen_vtc please fight for the most important race of your life! #keepfightingkeagz".
Girdlestone is considered a rising star who may have slipped through the grasp of New Zealand cycling, and is already embarking on a professional career.
The former Christchurch Boys High student was picked up by the new Dimension Data team, which cyclingnews.com said was formed to give African riders an opportunity to race in Europe. The Coppa della Pace was Girdlestone's second race in Europe. The final stage of the race was halted after the crash.
The Girdlestone family moved to Christchurch from Pretoria four years ago. Keagan Girdlestone, whose 26-year-old brother Dylan is also a professional cyclist, burst into prominence in 2014 as the youngest winner of the 100km Christchurch to Akaroa race when he was just 16. He finished fourth at the junior men's time trial in Virginia last year, riding under the South African flag. Success in Australia helped fast track him into the professional scene but tragedy has struck almost straight away.
The Italian site Tuttobiciweb reported race director Raffaele Babini as saying: "The accident occurred when there were four laps to go. We had covered 105km of racing. It was 16.20. The boy had fallen into a downhill section and was a strong recovery to return to the group. Apparently, after the first time, which was in the vicinity of a hill, a team car has slowed sharply and the guy, who was at full speed, crashed violently against the car, breaking through the rear window of the car, getting serious facial injuries. I cannot say more because they are still under investigation by the security forces."
Dylan Girdlestone posted: "Thanks for the support so far. Keep it up, he needs it. Still in very critical condition this morning as it was a rough night."