Morsi supporters responded, saying Gen. Abdel Fattah al-Sisi's nationally broadcast appeal amounted to a lead-up to civil war.
The Obama administration followed Sisi's call by saying it would at least temporarily halt a planned delivery of F-16 fighter jets to Egypt's military.
"I urge the people to take to the streets this coming Friday to prove their will and give me, the army and police a mandate to confront possible violence and terrorism," Sisi told military academy graduates in Alexandria in a speech carried live on state TV.
"The army and the police will secure the protests all over Egypt," said Sisi, who is also defense minister and first deputy prime minister.
"We will never retreat when it comes to the proposed road map of the political transition," he said.
Sisi asked protesters to refrain from violence, but he urged them to take to the streets on the same day Morsi's mostly Islamist supporters planned some 34 marches in Cairo.
The anti-Morsi Tamarod grassroots movement -- which brought millions out to protest against Morsi before his July 3 military ouster -- urged supporters through Facebook to follow the armed forces' call for protests.
It called on "all the Egyptian people to gather in all the squares" to "support the Egyptian armed forces in the coming war against terrorism and cleansing the land of Egypt."
"The army and the people will fight terrorism," the statement on Facebook said.
The military and other opponents of Morsi increasingly refer to the Muslim Brotherhood members as "terrorists."
The pro-Morsi National Coalition for Supporting Legitimacy, made up of 11 political parties including the Brotherhood's Freedom and Justice Party, told supporters ahead of their planned Cairo marches Friday it feared the military leaders would use the conflicting demonstrations to create violence against Egyptians who support the deposed president.
"The coalition is asking the international community and its institutions, including the U.N. and human rights organizations, to reject the plot for bloodshed that will inflame the region and is being executed by the leader of the coup, Abdel Fattah al-Sisi," the coalition said.
Amr Darrag, a Freedom and Justice Party leader and a former Morsi minister, told The Wall Street Journal he was clear about what Sisi was up to.
"He has tried all other means and he's failing," Darrag said. "He's trying to use the last card, which is threatening civil war. This is very dangerous."
Neither interim President Adly Mansour nor Prime Minister Hazem al-Beblawi had an immediate comment about Sisi's mass-protest call or the responses.
Mansour spokesman Ahmed al-Muslimani was quoted by state media Wednesday night as saying, "Egypt started the war on terrorism, and the call of General Sisi is to protect the revolution and the state."
Morsi hasn't been seen in public since his removal July 3. His family has accused the military of kidnapping him.
The military, ignoring calls from Western allies and the United Nations to release Morsi, says it is keeping him in protective custody for his own safety. Morsi hasn't been charged with a crime.
After Sisi's call, Egypt's public prosecutor announced arrest warrants for nine Brotherhood leaders, including the group's head, or general guide, on suspicion of inciting violence and enlisting armed protesters, the official Middle East News Agency reported.
Some of those leaders were arrested earlier and released on bail. Wednesday's announcement added new charges, the MENA report said.
Also Wednesday, Pentagon officials said the White House ordered at least a temporary halt to a scheduled delivery of four F-16s to Egypt.
The jets are part of a $2.5 billion order for 20 of the jet fighters Cairo placed with Washington in 2010.
The announcement reversed earlier Pentagon statements it would still make the delivery, despite political turmoil after Morsi's ouster.
"Given the current situation in Egypt, we don't believe it is appropriate to move forward at this time with the delivery of F-16s," Pentagon spokesman George Little told reporters.
U.S. officials said the suspension was unrelated to Sisi's appeal and wouldn't affect other types of aid or military cooperation.
Washington provides more than $1.3 billion to Egypt's military every year and hundreds of millions more in economic aid.
Secretary of Defense Chuck Hagel told Sisi about the jet holdup by phone after the Egyptian military leader's speech, a U.S. official told the Journal.
Washington still plans to go ahead with annual U.S.-Egyptian joint military exercises, known as Bright Star, officials said.