Keir Starmer told The Times newspaper people who want to help their terminally-ill loved ones to die should legally be allowed to.
He said people who wanted to end their lives shouldn't have to "traipse off to Switzerland" to do it.
His comments come two weeks before MPs debate potential assisted dying legislation in Parliament, which would allow a terminally ill person with six months or less to live to be prescribed lethal drugs if two doctors agree that the person had a "clear and settled intention to die".
A High Court judge would be able to intervene if necessary.
A Church of England spokeswoman said: "We believe that legalising assisted suicide would have serious consequences for the most vulnerable in our society.
"Far from being a progressive policy, such a change in the law would put two large groups of people at risk - those who would feel pressured to end their lives prematurely and those who would put pressure on themselves to do so.
"No amount of so-called 'safeguards' would protect thousands of people from such pressure."
