In a phone call with Egyptian vice president for foreign affairs, Mr Hague stressed the need for dialogue and reconciliation between all political parties including Mr Morsi's Muslim Brotherhood.
The Foreign Secretary also condemned the excessive use of force by security services as well as attacks against them.
Mr Hague said: "We want to see a peaceful resolution that will bring an urgent end to the current bloodshed. In my view, this should involve a process of dialogue and reconciliation between all political parties in Egypt, including the Muslim Brotherhood.
"I also called for the release of all political detainees, including President Morsi, unless there are criminal charges to be made against them, and emphasised that it is vital that any charges are not politically motivated."
More top news
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.
Scientists suggest that in 30 years antibiotic resistance will likely kill more people globally than cancer and diabetes combined.