The Egyptian military last week brought an end to the presidency of Mohammed Morsi barely a year after he was sworn in as the first democratically elected president in Egyptian history.
Morsi hails from the conservative Muslim Brotherhood. His administration was criticized for favoring Islamic political groups and for not doing enough to address Egypt's economic woes.
Hague told Parliament in London the British government does not condone military intervention in democratic processes but recognized the growing frustration with Morsi's government.
Interim Prime Minister Hazem Beblawi called for swift elections to reset the country's post-revolution political climate. The Muslim Brotherhood has so far rejected proposals offered since Morsi's ouster.
Hague said Morsi's administration failed to live up to the expectations of the people who took to the streets in 2011 to pressure longtime President Hosni Mubarak to step aside.
"The hunger and aspiration for a better Egypt is as strong and urgent as ever," he said Wednesday. "It is vital for their own country and the region that all sides rise above self interest and work toward an open, democratic and reforming Egypt."
Hague stressed there was "no alternative" to the long, painstaking process needed for democratic transition.
"Democratic change is a process, not an event," he said.