Morsi's administration has defended the decree as an effort to speed up reforms and complete a democratic transformation in the Arab world's most populous country.
"Calls for civil disobedience and strikes will be dealt with strictly by law and there is no retreat from the decree," Refa'a Al-Tahtawy, Morsi's presidential chief of staff, told the Al-Hayat private satellite channel.
But opponents say Morsi is behaving like a modern-day pharaoh, a jibe once levelled at Mubarak. The United States, a benefactor to Egypt's military, has expressed concern about more turbulence in a country that has a peace treaty with Israel.
"We don't want a dictatorship again. The Mubarak regime was a dictatorship. We had a revolution to have justice and freedom," 32-year-old Ahmed Husseini said in Cairo.
The fractious ranks of Egypt's non-Islamist opposition have been united on the street by crisis, although they have yet to build an electoral machine to challenge the well-organised Islamists, who have beaten their more secular-minded rivals at the ballot box in two elections held since Mubarak was ousted.
"There are signs that over the last couple of days that Morsi and the Brotherhood realised their mistake," said Elijah Zarwan, a fellow with The European Council on Foreign Relations. He said the protests were "a very clear illustration of how much of a political miscalculation this was".