Archbishop Emeritus Desmond Tutu has come out in support of euthanasia after Sean Davison, founder of right-to-die organisation DignitySA, was arrested for murder.

Davison was arrested on Tuesday in connection with the death of his friend Anrich Burger in 2013. Burger became a quadriplegic in a car crash.

He was granted R20 000 bail on Wednesday, which included conditions, such as only leaving the Western Cape with the police's consent and reporting to a police station once a week.

"Just as I have argued for compassion and fairness in life, I believe that terminally-ill people should be treated with compassion and fairness when it comes to their death," Tutu said in a statement on Friday.

"This should include affording people who have reached the end stages of life the right to choose how and when to leave Mother Earth."

Tutu encouraged policymakers to engage, enable and regulate assisted suicide.

On the allegations, DignitySA co-founder Willem Landman said: "The organisation is on record that we stand for changing the law in South Africa to conform with the Constitution and... we do not assist people to die.

"What anyone does in their private capacity is their own matter."

On Wednesday, prosecutor Megan Blows said new information had "come to light... the accused might have committed other similar offences".

Davison maintained his innocence in court.

"It is and has always been my contention that I have not committed any offence as alleged in this matter," his lawyer Joshua Greeff read from an affidavit.

He is expected back in court on November 16.

Davison, a professor, also helped his mother end her life in New Zealand.