The decision to give victims of crime the right to appeal against decisions not to charge was prompted by a Court of Appeal ruling involving a 2007 case in which the CPS decided not to bring sexual assault charges.
The decision was reversed by the Court of Appeal and in 2011 disabled man Christopher Killick was jailed for three and a half years for sexually abusing two fellow cerebral palsy sufferers.
The court stated "as a decision not to prosecute is in reality a final decision for a victim, there must be a right to seek a review of such a decision".
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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.