He also repeated his view that the palliative care system was not "where it needs to be to give people a real choice".
Proposals in the bill, which was put forward by Labour MP Kim Leadbeater, would give terminally ill people in England and Wales the right to end their life.
Scotland is also considering changes to the law.
MPs at Westminster will be given a free vote, meaning they can choose based on their own conscience rather than having to follow a party line.
Streeting said the government would "respect and act upon" the outcome of the vote on the "incredibly difficult and complicated issue".
