It was unclear whether intense sports rivalries or political strife caused the clashes in the northeastern city of Port Said.
Hours after the fighting, protesters in Cairo chanted, "Down with military rule." And the secretary-general of the Muslim Brotherhood party blamed Egypt's military for the deaths.
Egypt's interior ministry blamed fans for provoking police.
A committee will investigate the circumstances surrounding the fighting, the Supreme Council of the Armed Forces said in a statement early Thursday.
The clashes left at least 74 dead, Egypt's health ministry said in a statement. At least 1,000 people were injured, 150 of them critically, ministry spokesman Dr. Hisham Shiha said. Most of the injured had concussions and deep cuts, he said.
The fighting occurred in a stadium in Port Said after the home Al-Masry team beat Cairo's Al-Ahly team 3-1.
Fans from both sides bashed each other with rocks and chairs, said Mohamed Sultan, head of the ambulance association in Port Said.
Many of those who died fell from bleachers inside the stadium, according to Ahmed Saeed, an official from the Port Said governor's office.
Others suffocated, said Al-Ahly fan Amr Khamis, who returned to Cairo early Thursday with his head bandaged after an Al-Masry fan beat him with a wooden stick.
"The police opened the gates separating us from the Masry fans and their hooligans attack us with everything: rocks, glass bottles, knives, swords. Some had guns. ... How did the police allow them with these weapons into the bleachers?" he said.
Authorities contributed to escalating violence, said Mamdouh Eid, the executive manager of the Al-Ahly fans committee.
"The police stood there watching, and the ambulances arrived late. I carried several dead fans in my arms," he said.
Tension was building throughout the game, Eid said, as Port Said fans threw bottles and rocks at players.
"There were organized groups in the crowds that purposely provoked the police all through the match and escalated the violence and stormed onto the field after the final whistle," said Gen. Marwan Mustapha of Egypt's interior ministry. "Our policemen tried to contain them, but not engage."
At least 47 people were arrested after the clashes, he said.
The interior ministry and the military were not responsible for what happened, Gen. Ismail Osman, a member of Egypt's military council, told Mehwar TV.
"Security is lacking now more than ever before. The government must be more stringent," he said.
Many Al-Ahly fans were trapped in the bleachers during Wednesday's fighting, Eid said, because police did not open gates that would have allowed them to exit the stadium.
"Some fell off bleachers, others suffocated, and many were beaten to death and stabbed by knives," Eid said.
When the clashes broke out, about 22,000 people were inside the stadium, which can hold up to 25,000 people. About 2,000 Al-Ahly fans were at the game, he said.
Authorities have been dispatched to hospitals to interview the wounded and investigate, said Adel Saeed, a spokesman for Egypt's general prosecutor.
Egypt's military deployed two planes to transport the Al-Ahly team, some of its fans and some of the injured back to Cairo, he said.
Thousands of demonstrators met a train carrying injured Al-Ahly fans returning to Cairo early Thursday. Some demonstrators climbed on top of the train as injured fans were carried out. Port Said is about 125 miles (200 kilometers) northeast of Cairo.
Outside the Al-Ahly club's headquarters, angry fans vowed revenge.
"This is a plot to stir violence in Egypt. Why would a winning team attack others ... and kill them? We will not let this one go," Al-Ahly fan Ahmed Tabaei said.
Protesters outside the club chanted, "Down with military rule; leave it to civilian rule."
The head of Egypt's military ruling council declared three days of national mourning, starting Thursday, and said those behind the clashes would be punished.
"This period, I assure you, will be peaceful. Egypt will be stable again. The military council is executing a road map to transfer the authority to an elected civilian entity. ... Whoever has any plot against Egypt will not succeed," Field Marshal Mohamed Tantawi said in a statement released to Egyptian media.
The Muslim Brotherhood condemned the violence and said authorities had failed to protect citizens.
"It's a security vacuum in the whole country that has led to armed robberies on banks and random killings. Some have threatened rebellion against the parliament and threatened the youth of the Muslim Brotherhood ... which may indicate that some police officers may be punishing the citizens for causing a revolution," the party said in a statement.
While authorities were responding to the fighting in Port Said, a fire broke out during a match in a Cairo stadium. It was not immediately clear whether the incidents were related.
Lawmakers were scheduled to discuss the situation in an emergency session of Egypt's parliament Thursday.
Sepp Blatter, president of the sport's international governing body, FIFA, said he was "very shocked and saddened" by the events.
"This is a black day for football. Such a catastrophic situation is unimaginable and should not happen," Blatter said in a statement.
The large death toll from the fighting is unprecedented in Egyptian soccer, CNN contributor James Montague said.
"It's not unheard-of to have organized violence between football clubs (in Egypt), but something on this scale has never been seen before," said Montague, who researched soccer in the Middle East for his book "When Friday Comes: Football in the War Zone."
During Egypt's revolution, well-organized groups of soccer fans became a powerful force for political change, he said. Soccer was also closely tied with former Egyptian President Hosni Mubarak's government, which used the sport to boost his popularity, Montague said.
But it was unclear whether political fury fueled Wednesday's clashes.
"There's been a security vacuum, so we don't know whether it's that or whether there's a Mubarak element to it. We just don't know at the moment," Montague said.
