Nour's al-Ghad Party issued a statement on Tuesday signed by 14 groups including the Egyptian Organisation for Human Rights that said Nour's trial had "become a means to oppress him and punish him for his political views".
Nour was detained on 5 December as his trial on forgery charges neared its conclusion. He has pleaded not guilty to ordering the forging of signatures to register his party last year and faces a maximum prison sentence of 15 years.
"We call for his immediate release since his imprisonment, despite his health condition, is considered unjustifiable obstinacy," said the statement.
Nour, a diabetic, was taken on Saturday to a hospital inside the Tora prison after his health condition deteriorated after starting a hunger strike to protest his detention.
His trial resumes on Saturday.
His 29 January arrest and subsequent 42-day detention without charge strained US-Egyptian relations. He finished a distant second to longtime President Hosni Mubarak in a heated September election and lost his parliament seat in November polls.