CLAAS, a charity which helps persecuted Christians in Pakistan, has said the bail application was rejected as the group were accused of involvement in a 'lynching' on the city's Metro.
The organisation will appeal the decision within 30 days, it said.
Police are accused of arresting the Christians without "any proof or evidence" by CLAAS which added that the government was "not paying any attention, or trying to resolve this ongoing situation".
The group deny involvement in the attack and last month 10 other Christians accused of the same assault were granted bail.