The US citizen, a 21-year-old who reportedly worked for an American cultural centre in Alexandria, was killed as he took photographs of the demonstration, officials said.
The unrest is seen by many as a prelude to mass anti-Morsi protests planned for Sunday, the first anniversary of his becoming president, prompting appeals for calm from the United States.
An official at the US embassy in Cairo told AFP: "We have heard of reports of the death of a US citizen. We are seeking to confirm."
Egyptian health ministry and security sources said the American, whose name has not yet been released, was stabbed, although a medical official said earlier he had died of birdshot wounds.
Clashes also erupted in the Nile Delta provinces of Daqahliya and Beheira, security officials said, adding that at least 130 people were injured nationwide.
The violence during rival rallies raised fears of widespread violence on the first anniversary of the Islamist leader's inauguration.
Fervent displays of emotion on both sides underline the bitter divisions sweeping Egypt, with Morsi's opponents accusing him of hijacking the 2011 revolution and his supporters vowing to defend his legitimacy to the end.
The offices of the Freedom and Justice Party, political arm of Morsi's Muslim Brotherhood, were torched in Alexandria and at Aga in the Nile Delta province of Daqahliya, security officials said.
FJP offices in Beheira were also stormed, they said.
At least four people have also died since Wednesday in clashes in the Nile Delta -- three in Mansura city and one in Zagazig, medics said.
Overnight violence was also reported in the eastern part of the Delta, north of the capital, Morsi's own home province of Sharqiya.
"We urge all parties to refrain from violence and express their views peacefully. And political leaders have the responsibility of taking steps to ensure that groups do not resort to violence," US State Department spokesman Patrick Ventrell said.
In "our opinion, all Egyptians have the right to express their opinions and concerns freely. We've urged the government to protect that right."
Germany warned Egypt's fledgling democracy faces a "moment of truth", and urged Morsi to implement reforms.
In Cairo, tens of thousands of Islamists gathered under the slogan "legitimacy is a red line", referring to Morsi's insistence that he has a popular mandate.
"We will not allow a coup against the president," senior Brotherhood leader Mohamed al-Beltagui told the crowd.
Anti-Morsi protesters joined hundreds camped overnight in Tahrir Square, epicentre of the 2011 revolt that toppled Hosni Mubarak and catapulted the Islamist to the presidency.
Thousands more anti-Morsi protesters demonstrated across Cairo, while his opponents also gathered in Alexandria, Mansura and the canal city of Port Said.
The June 30 protest was called by Tamarod (Arabic for Rebellion), a grassroots movement which says it has more than 15 million signatures for a petition demanding Morsi's resignation and a snap election.
The broad-based opposition alleges Morsi reneged on his promise to be a president for all Egyptians and has failed to deliver on the uprising's aspirations for freedom and social justice.
Morsi himself warned in a televised speech this week that the growing polarisation threatened to "paralyse" Egypt.
He pledged to consider constitutional reforms and appealed to the opposition to join talks.
It was his latest attempt to strike up a dialogue between political factions in a country deeply split between his Islamist allies and an opposition of leftists, liberals, Christians and some Muslim groups.
On Thursday, the opposition National Salvation Front coalition rejected his offer of talks and renewed its call for a snap presidential election.
Since taking office last June 30, Morsi has squared off against the judiciary, media, police and even artists.
But he has also admitted to failings.
"I have made many mistakes, there is no question. Mistakes can happen, but they need to be corrected," he said.
He also warned the media against abusing freedoms won in the uprising.
The army, which oversaw the transition from Mubarak's autocratic rule but has been on the sidelines since Morsi's election, has warned it would intervene in the event of violence.
It has brought in reinforcements to key cities, security officials said.