Members of the Muslim Brotherhood have been protesting near the Republican Guard headquarters since Morsi was removed from office, amid speculation he may be under house arrest at the site.
Morsi was ousted by Egypt's military last week just one year into his four-year term in the wake of huge protests demanding that he quit. The Islamist was replaced by an interim leader and new elections have been promised but no timeline has been announced.
A statement by the Brotherhood-linked Freedom and Justice Party said more than 53 had been killed and 1,000 injured.
"Early on Monday, supporters of the legitimate elected President Mohammed Morsi performing the dawn prayer outside the Republican Guard headquarters were massacred with heavy gunfire, live bullets, birdshot and tear gas," the party said in a statement on its website.
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Witness Al-Shaimaa Younes, who was at the sit-in, told The Associated Press that troops and police forces opened fire on the protesters during early morning prayers.
"They opened fire with live ammunition and lobbed tear gas," she added. "There was panic and people started running. I saw people fall."
Turkish Foreign Minister Ahmet Davutoglu also condemned Monday's incident as a "massacre," Reuters reported.
"I strongly condemn the massacre that took place in Egypt at morning prayer in the name of the fundamental human values which we have been advocating,'' Davutoglu said on Twitter.
British Foreign Minister William Hague issued a statement condemning "the violence that led to the deaths of over 40 people during demonstrations in Egypt overnight." He also called for the release of detained political leaders and journalists.
At least 35 people also died in violence on Friday and Saturday in violence that came two and a half years after autocratic ruler Hosni Mubarak was toppled in a 2011 uprising.
—The Associated Press and Reuters contributed to this report.