At least 33 marches were held in Cairo and Giza under the slogan "Egypt against the coup," Ahram Online reported. Protesters turned out in other cities, including Alexandria.
There were no reports of the kind of violence that has killed scores of people, mostly Morsi supporters, in recent weeks. The military has said it will break up protest camps set up by pro-Morsi demonstrators.
The show of support for Morsi came after U.S. Secretary of State John Kerry told a Pakistani broadcaster the military had restored democracy by toppling Morsi, a leader in the Muslim Brotherhood.
"The military was asked to intervene by millions and millions of people, all of whom were afraid of a [descent] into chaos, into violence," Kerry told private Geo TV in Pakistan while visiting Islamabad.
"And the military did not take over, to the best of our judgment -- so far," Kerry said. "To run the country, there's a civilian government. In effect, they were restoring democracy."
His comments echoed those of Egyptian Defense Minister Gen. Abdel Fattah al-Sisi, who has said he was carrying out the people's will by overthrowing Morsi July 3. He said the people demanded a new and more inclusive constitution, new presidential elections and a new leadership to replace Morsi's Islamist-leaning government.
Kerry's comments were the strongest public U.S. approval yet of the military intervention, which the Obama administration has declined to call a coup.
Calling it a coup would require Washington to suspend its annual $1.5 billion aid package, a move U.S. officials say would further destabilize Egypt. The administration said last week it was not legally required to determine whether the military had engineered a coup.
The administration's official position has been it doesn't support Morsi's overthrow and seeks a quick restoration of civilian rule in Cairo.
"He did not stick to the script," a U.S. official told The Wall Street Journal, referring to Kerry's comments.
Kerry said last month Egypt might have avoided a civil war by ousting Morsi.
Many Morsi supporters already accuse the United States of supporting a coup to suppress Egypt's Islamists. They say Washington wants democracy to spread, but in a U.S. way, without Islamist political parties.
Kerry told Geo TV he was concerned about Egypt's turmoil, saying he told top Egyptian officials, including Sisi, the violent crackdown was "absolutely unacceptable."
"It cannot happen," he said.