It comes as a demonstration was held outside the House of Lords by campaigners from groups such as 'Christian Concern' and 'Not Dead Yet UK'.
Peers are considering amendments to Lord Falconer's 'Assisted Dying Bill', which would allow medical professionals to be able to assist terminally ill people to end their life.
Most Revd Justin Welby questioned the argument that it would be 'compassionate' to allow the bill, on the basis that it could end terminally ill people's suffering.
In an article written for The Times newspaper, he pointed out that, 'compassion literally means 'to suffer with'.
He wrote: "The problem with the argument is not that it fails to show compassion, but that it fails to show enough compassion. It restricts compassion to the immediate and the personal instead of extending it to everyone. It fails to recognise the truth contained in the parable of the Good Samaritan: every person is my neighbour; every person deserves my compassion.
"It is entirely understandable that when we see someone we love suffering we will suffer along with them and we will want to do almost anything to alleviate their suffering. Even in the face of such agony, I would make a plea that the deep personal demands of one situation do not blind us to the wider needs of others."
The Assisted Dying Bill is currently at Committee stage, which means Parliament would still need to approve the bill before it could be made law.
Campaign group 'Dignity in Dying', however claims that the bill does have safeguards and would provide choice to suffering patients with no chance of recovery over how and when they die.
It argues that patients would have to meet clear pre-determined criteria and have explored all their alternatives before being considered. The group claims the bill:
- "Would not legalise assisted suicide for people who are not dying (for example disabled people or older people).
- "Would not legalise voluntary euthanasia where a doctor administers the life-ending medication. Under the Assisted Dying Bill the person choosing an assistance to die would self-administer the prescribed life-ending medication.
- "Would not legalise a system where the person being directly helped to die is no longer competent to make that choice for themselves. This Assisted Dying Bill would only apply to adults with mental capacity both at the time of their request and at the time of their death"
Dr Kevin Fitzpatrick, who's a spokesperson from 'Not Dead Yet UK' argues that there is no need for a change in the law:
"The law as it stands does not stop anyone committing suicide, however they do it. What it does is, it protects them from abuse.
"So, if someone says 'I want to die' and someone says 'well, I'll help you' then what the law does at the moment is it stops them and makes them think - So that no one does this in any way flippantly, lightly or for any other reason that this is a genuine, serious determined wish at the end of someone's life. They already can do that."
Disability activist, Dennis Queen says she has concerns about what this bill represents, in terms of society's attitudes towards sick, dying and disabled people:
"If we are sick and we are depressed, and if we are suicidal, we want to same help and the same protection that the law offers everybody else.
"I still think that most of the public do care about what people like me are going through and if they hear us they might stop believing the very vocal, few disabled people who want this suicide pill and start listening to the fact that most of us who are affected by it are already living with risk every single day and fighting for the things that we need.
"Our lives still have value and we will fight this bill every time they bring it back."
It comes as a poll has found more than four in five doctors specialising in end-of-life care say they do not want to be involved in ending a terminally ill patient's life.
A majority of members of Association for Palliative Medicine said courts, not doctors, should decide which patients can end their life, and then employ technicians to do it.
4% of doctors in the poll said would be willing to help a dying patient end their life.
Listen to disability activist Dennis Queen speaking outside the House of Lords: