His remarks come as the House of Commons is set to debate a proposal to legalise the practice.
Speaking at the Financial Times Weekend Festival in London on Saturday, Mr Streeting spoke about the importance of making sure “people aren’t coerced into exercising their right to die” because of a lack of support in end-of-life care.
He said having the “right protections and safeguards” in place was needed to make sure people don’t “take their own life thinking they were a burden on others”.
He added: “That is one of the reasons why I can buy into the principle and think about people in my own life who have really suffered at the end of life and not want to impose my views on assisted dying as to whether they should have a choice.
“But I am not sure as a country we have the right end-of-life care available to enable a real choice on assisted dying.”