The sources said that an Egyptian protester and a young US cameraman were killed in the deadly clashes in the port city of Alexandria on Friday.
They stated that the Egyptian was shot and the American was stabbed in the chest near the headquarters of the Muslim Brotherhood, which was set on fire by anti-government protesters.
More than 160 people were also injured during the clashes in Alexandria, Health Ministry spokesman Yahya Moussa said.
According to the Muslim Brotherhood’s Freedom and Justice Party, one person was killed in Morsi’s hometown, Zagazig.
One demonstrator was killed and five were others wounded after a gas cylinder exploded among protesters in the northeastern city of Port Said.
The Brotherhood said anti-government protesters had attacked and ransacked eight of its offices across the country.
In the capital Cairo, tens of thousands of pro- and anti-government protesters held separate demonstrations. The protests largely remained peaceful in Tahrir Square, around the Defense Ministry and in front of the presidential palace.
Earlier in the day, Egypt's leading clerics warned of "civil war" and appealed for calm as tension grew ahead of mass rallies planned by opposition to unseat Morsi.
"Vigilance is required to ensure we do not slide into civil war," clerics from Egypt's leading Muslim authority, the Al-Azhar institute, said in a statement.
The academy, which is one of the most influential centers of scholarship in the Muslim world, backed Morsi’s offer of dialogue and blamed "criminal gangs" who attacked mosques for street violence.
The Brotherhood accused liberals, who were once loyal to ousted dictator Hosni Mubarak, for inciting violence by hired "thugs".
The United Nations, the European Union and the United States have all appealed for restraint and called on the North African country’s political leaders to step back from the confrontation.
In a televised address on Wednesday, Morsi warned that polarized state of the country's politics is "threatening to paralyze” Egypt.
He acknowledged that he made some mistakes during the first year of his presidency but called for national reconciliation, saying that he was open to cooperating with the opposition on constitutional reform.
On Thursday, Egypt's main opposition coalition -- the National Salvation Front (NSF) -- rejected the president’s offer and called instead for early elections.
The NSF claimed that Morsi had failed to take responsibility for the country's deep political polarization and failed economy.
The opposition group Tamarod (Arabic for Rebellion) has called for mass demonstrations on Sunday, which marks Morsi’s first year in office, to demand his resignation and early presidential elections.
Meanwhile, troops have been deployed across Egyptian cities ahead of the planned protests.
Several political groups say the government is dominated by the Brotherhood. The opposition also accuses Morsi of deviating from the 2011 revolution that toppled the Western-backed regime of Mubarak.
Morsi’s supporters, however, say the president is cleansing Egyptian institutions of corruption. They also believe that he needs time to put into practice the principles of the 2011 revolution.
Egypt has witnessed continuing anti-government protests since Morsi took office in June 2012 in a landmark election held following the ouster of Mubarak.