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
Ahead of Hillary Clinton's historic clash with Donald Trump, we look at key moments that changed election outcomes.
An ejector seat manufacturer is to be prosecuted over the death of Red Arrows pilot Sean Cunningham at RAF Scampton in November 2011.
Police said the "active shooter", reportedly a lawyer, had since been shot by officers and they were not seeking any other suspects.