The Pole was operated on for seven hours by two teams of surgeons on Sunday when he sustained multiple fractures to his right hand, leg and arm after a high-speed crash in a minor rally in Italy.
The big concern at the time, apart from considerable blood loss, concerned his right hand with Kubica's forearm cut in two places with significant lesions to the bones and tendons.
Kubica is one of Formula One's brightest prospects, a good friend of Ferrari's Fernando Alonso and Renault's leading driver.
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"On Thursday, Robert should undergo some more surgery in order to stabilise the fractures to his right shoulder and right foot," the Lotus-backed team said in an update on the 26-year-old's progress.
"Three or four days later, another operation will allow his elbow fracture to be stabilised as well."
Renault said Kubica's general condition had continued to improve overnight.
"According to the doctors, the levels of inflammation are in the norm considering his medical condition, and the recovery of his forearm remains encouraging.
"Yesterday, Robert was able to talk to his doctors and relatives. His medication makes him sleep quite a lot, but he is responding to all external stimulation," the team added.
"He has reacted well to the news about his condition and is ready to fight for his comeback."
Renault said Kubica was likely to stay at the Santa Corona Hospital near Genoa for two to three weeks before a decision was taken about where he should continue his rehabilitation.
The season starts in Bahrain on March 13 with Renault resigned to losing him for at least the first two months and possibly the entire championship.
No replacement has been named.
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