The singer, who is being treated in hospital in Vienna, Austria, is said to be responding to treatment and "slowly improving".
He had been joined by his 75-year-old father Kyriacos Panayiotou, who is known as Jack Panos, as well as sisters Melanie, 49 and Yioda, 53.
His former boyfriend, art dealer Kenny Goss, is also due to join the group in the Austrian capital shortly.
The 48-year-old starâs boyfriend, hair stylist Fadi Fawaz, has kept a bedside vigil since the singer fell ill on Monday of last week.
Fawaz, 38, reportedly appeared tired and drawn as he left the hospital over the weekend. He was accompanied by two women, believed to be Michaelâs sisters, one of whom held her head in her hands waiting in the hospital lobby.
The Daily Mail quoted a "close friend", who said: "His whole family are with him. They are very close-knit. George is just such a lucky man in that sense. Heâs so adored."
Speaking of 53-year-old Goss, Michaelâs partner for 13 years until 2009, the friend added: "Kenny of course is very concerned. He has been in touch every day. They will always be the best of friends."
Michael, who has pulled the plug on the rest of his tour, has been told by doctors to take "complete rest" and the remainder of his scheduled shows have been put on hold.
The star, who has been diagnosed with "community acquired pneumonia", was due to play British shows on his Symphonica tour until the week before Christmas.
His publicist said earlier this week: "He is receiving excellent medical care; he is responding to treatment and slowly improving."
Doctors said they could not estimate how long he would need to recover.
It is the latest medical setback during the tour, his first for three years after previously saying he was to quit playing live. Just a month ago he was forced to pull out of an appearance at the Royal Albert Hall due to a viral infection and high temperature.
Michael, 48, spent a month in prison for drug driving last year.
Specialists in Vienna, Dr Christoph Zielinski and Dr Thomas Staudinger, issued a statement today saying: "George Michael has severe community acquired pneumonia and is being treated as an inpatient. His condition has stabilised and he is responding to treatment.
"From the current point of view, the time until recovery cannot be estimated, but he will not be able to perform the rest of the tour. Besides medical treatment, complete rest and peace and quiet are mandatory."
Promoters are working to rearrange the postponed dates "at the earliest opportunity".
The tour began in Prague in August and has so far seen him play 45 shows in 35 cities.
A hospital spokesman declined to comment on the singerâs latest condition on Monday.