Sir Keir Starmer is confident an assisted dying law can work, despite Health Secretary Wes Streeting saying there is no budget for it.
The Prime Minister insisted the correct preparation has been done to ensure the Bill is “workable in all its aspects”.
Sir Keir supported the Terminally Ill Adults (End of Life) Bill in a historic vote on Friday which saw the proposed legislation clear the Commons.
The Government is neutral on the topic and MPs had a free vote, meaning they made their own decisions rather than following party lines.
Mr Streeting was one of the most senior Government ministers to vote against the Bill, alongside Justice Secretary Shabana Mahmood and Deputy Prime Minister Angela Rayner.
At the weekend, Mr Streeting warned that legalising assisted dying would take “time and money” away from other parts of the health service.
He said better end-of-life care was needed to prevent terminally ill people feeling they had no alternative but to end their own life.
Writing on his Facebook page, Mr Streeting said: “Even with the savings that might come from assisted dying if people take up the service – and it feels uncomfortable talking about savings in this context to be honest – setting up this service will also take time and money that is in short supply.
“There isn’t a budget for this. Politics is about prioritising. It is a daily series of choices and trade-offs. I fear we’ve made the wrong one.”
Sir Keir was asked by reporters if the will of Parliament must be implemented and a budget found for assisted dying.
He said: “It is my responsibility to make sure the Bill is workable, and that means workable in all its aspects.
“I’m confident we’ve done that preparation.”
The Bill cleared the Commons on Friday, but with a narrower majority of 23 votes, compared with a majority of 55 in November.
It will next come before the House of Lords for further debate and votes.
Labour MP Kim Leadbeater, who steered the Bill through the Commons, has said she hopes peers will not try to derail the legislation, which could run out of parliamentary time if it is held up in the Lords.
Speaking in the aftermath of the Commons vote, she said: “I would be upset to think that anybody was playing games with such an important and such an emotional issue.”
The proposed legislation would allow terminally ill adults in England and Wales, with fewer than six months to live, to apply for an assisted death, subject to approval by two doctors and a panel featuring a social worker, senior legal figure and psychiatrist.
