The Hawkeye star - who recently celebrated his 52nd birthday in a hospital bed - suffered severe injuries to his chest and back while clearing snow from outside his family home near Lake Tahoe, Nevada on New Year's Day.
Kym Renner told People: "We are so thrilled with his progress. If anyone knows Jeremy, he is a fighter and doesn't mess around. He is crushing all the progress goals. We couldn't feel more positive about the road ahead."
The Avengers star lost a serious amount of blood, suffered blunt force chest trauma and orthopaedic injuries, and underwent surgery after he was accidentally run over by a snow plough which he had been using to clear a heavy snow fall outside his home.
Watch: Jeremy Renner has posted from his hospital bed
Renner has been sharing updates with fans from his hospital bed, telling his 19.5m followers: "Thank you all for your kind words. Im too messed up now to type. But I send love to you all."
TMZ reported that it had obtained the 911 emergency call log from the accident.
It said the Hurt Locker actor was "completely crushed" by the plough and that afterwards he was having "extreme difficulty" breathing and suffered heavy bleeding.
His Lake Tahoe house had been blocked in by the heavy winter weather and ended up being air lifted to hospital after attempting to clear an exit for his family.
A statement from the Marvel star's reps earlier this week read: "We can confirm that Jeremy has suffered blunt chest trauma and orthopaedic injuries and has undergone surgery today, January 2nd 2023.
"He has returned from surgery and remains in the intensive care unit in critical but stable condition.
"Jeremy’s family would like to express their gratitude to the incredible doctors and nurses looking after him, Truckee Meadows Fire and Rescue, Washoe County Sheriff, Reno City Mayor Hillary Schieve and the Carano and Murdock families.
"They are also tremendously overwhelmed and appreciative of the outpouring of love and support from his fans."
The Lake Tahoe area was hit by a heavy snow storm on New Year's Eve, leaving a reported 35,000 homes without power.
Renner has a nine-year-old daughter with his ex-wife Canadian model Sonni Pacheco.