Demonstrators outside Cairo's main government buildings demanded Morsi be returned to power, Voice of America reported.
"I have come here to protect my vote. I went out to vote in five elections. And then they just trampled on it. So let's go down their path -- how can we be sure the army won't take power again? It's unacceptable. We are willing to die here," one protester said.
Demonstrations are expected to peak when Muslims break their Ramadan fast with the evening meal.
Minor scuffles were reported at the protest outside the Cabinet building, Ahram Online, the Egyptian government's newspaper, reported.
A march, as it passed through the Manial area of Cairo, was tense but there was no reported violence, an eyewitness told Ahram.
Clashes between Morsi supporters and security forces left seven people dead and more than 260 injured overnight Monday.
The Muslim Brotherhood called for renewed protests Wednesday as a new government led by interim Prime Minister Hazem el-Beblawi began work, officials said.
El-Beblawi's newly formed Cabinet includes liberals and technocrats, including seven members of the previous government, VOA said.
It does not, however, include any members of Islamist parties such as the Muslim Brotherhood.
Thousands of supporters of Morsi, a member of the Brotherhood, have maintained a vigil at a Cairo square, demanding he be returned to office.