A spokesman for the group said: "They are devastated and are immediately planning to return to Great Britain.
The crush happened after about 1,500 fans turned up at a record store in the Taman Anggrek shopping centre to see the group.
The four-piece group have cancelled their tour of Asia and are returning to the UK after learning of the accident.
A spokesman for the group said: "They are devastated and are immediately planning to return to Great Britain.
"They have cancelled the rest of the tour and their thoughts are with the families and friends of those killed and injured."
Security guards at the shopping mall said panic broke out when fans tried to escape the crush by rushing to the mall's exits.
A hospital official said the four girls had died after falling during the stampede.
Two others are in a critical condition in hospital.
The group is made up of singers Mark Read, Ben Adams, Christian Ingebrigtsen and Paul Marazzi.
They last year had a UK number one with a cover of the 1980s A-ha hit Take On Me and won Best Newcomers at the Brits.
They were performing at the mall but left after they became concerned about security.
The group then went ahead with a live appearance on a local TV station.
They reportedly learned about the deaths five hours later.
Foreign pop groups rarely visit Indonesia, which is suffering from serious social and economic problems.
In the Philippines, the group had to cancel an appearance at a record store after 20,000 fans turned up when organisers were expecting only 1,000.