Former News International chief executive Rebekah Brooks, 44, from Churchill, Oxfordshire, also appeared at the Old Bailey charged with conspiracy to commit misconduct in a public office.
The matter was adjourned until next month.
Sun chief reporter John Kay, 69, from north-west London, entered a not guilty plea to conspiracy to commit misconduct in public office.
The cases have been brought as part of Operation Elveden, Scotland Yard's investigation into alleged inappropriate payments and information leaks.
In a separate case, a former police officer pleaded guilty to misconduct in public office.
And in another matter, a public official admitted misconduct in public office.
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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.