Council leader Barrie Grunewald is “on the road to recovery”, a Labour Party spokesman has said.
Coun Grunewald is in an induced coma after suffering a heart attack while on holiday in Gran Canaria.
The 37-year-old’s family have travelled to the Spanish resort to be by his side.
A Labour spokesman said: “Councillor Grunewald is in a stable condition and while it remains serious he is on the path to recovery.”
Leading politicians across the borough have sent get well soon messages to the stricken Labour leader.
Chief executive Mike Palin said: “Family and friends of the leader travelled to Gran Canaria on Sunday to be by his side.
“The council is receiving regular updates on the leader’s condition and further information will be provided when available – with due respect given to what is a sensitive situation.
“The thoughts of all at the council are with the leader, his family and his friends at this time.”
Coun Grunewald has enjoyed a long career in local politics, starting as an aide to former MP Shaun Woodward.
Deputy council leader Andy Bowden has temporarily taken on some of Coun Grunewald’s decision making duties.