Spokesman Doug Wright said he was able to nod and communicate with his family who have held a constant vigil at his bedside in a central London hospital.
The 62-year-old fell into a coma after contracting pneumonia in his battle against colon and liver cancer.
Gibb's wife, Dwina, has revealed he cried when she played him Roy Orbison's 1962 song "Crying."
Fellow Bee Gees star Barry Gibb had also been singing to his brother to try to rouse him.
Dwina Gibb told her local paper, The Impartial Reporter, based in Enniskillen, Northern Ireland, their children Robin John, Spencer and Melissa have been playing him music to "try and bring him back to us."
In February, Gibb said he had made a "spectacular" recovery from cancer but was later back in hospital for surgery.
The British-born singer had surgery on his bowel 18 months ago for an unrelated condition, but a tumor was discovered and he was diagnosed with cancer of the colon and later of the liver.
It had been thought his cancer was in remission as early as last month.
Robin Gibb's musical career began when he formed the Bee Gees with his brothers Barry and Maurice in 1958.
The group is among the biggest-selling groups of all time with hits spanning six decades, including "Stayin' Alive," "How Deep Is Your Love", "Massachusetts," and "Words."
Their soundtrack to the film "Saturday Night Fever" was one of the best-selling albums of the 1970s and the band has won seven Grammy awards.
Robin's twin brother, Maurice Gibb, died in 2003 at 53, due to complications from a twisted intestine.
His younger brother Andy, who had a successful solo career, died of a heart ailment in 1988; he was 30.
Gibb last performed on stage at the London Palladium in February, supporting injured servicemen and women in a charity concert.