The assisted suicide bill was "stacked round with safeguards" to prevent a sick or elderly relatives from being "pushed into death", one campaigner told Good Morning Britain.
Prue Leith, who lost her brother to bone cancer, said she was "not asking for euthanasia" but wanted to give the terminally ill the option of a peaceful death.
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The letter was signed by the CBI, British Chambers of Commerce, the EEF, the Institute of Directors and the Federation of Small Businesses.
A spokesperson said Rory Stewart's remarks were in line with the British government’s stated position.
The minister's intervention will come a week after Trump decertified the landmark agreement claiming it was not in the US national interest.