The Brotherhood, which has refused to accept the overthrow of its champion Mohamed Morsi, Egypt's first freely elected president, slammed the transition blueprint as an attempt to salvage last week's coup which would do nothing to end an increasingly bloody conflict.
The army warned it would brook no disruption to what it acknowledged would be a "difficult" transition.
The blueprint unveiled by caretaker President Adly Mansour is intended to replace the controversially drafted constitution which he suspended following last week's coup.
A committee will be set up to make final improvements to the draft before it is put to a referendum.
Parliamentary elections will then follow within three months and Mansour will announce a date for a presidential election once the new parliament has convened.
Hours after its unveiling, Mansour named a vice president and a prime minister, his spokesperson Ahmed al-Muslimani said.
The military has come under huge international pressure to swiftly install an interim civilian administration, pressure that has only intensified since gunfire killed 51 Muslim brotherhood protesters outside a Cairo army base on Monday.
Former finance minister Hazem al-Beblawi was named prime minister. Former UN nuclear watchdog chief Mohamed ElBaradei, a Nobel Peace laureate, was named vice president for foreign affairs.
Even though ElBaradei was its designated negotiator in talks on the transition, the grassroots Tamarod campaign which organised the mass protests that led up to Morsi's overthrow complained it had not been consulted on the transition plan.
Tamarod spokesperson Mahmud Badr said the movement would make proposals for changes to the blueprint, which it would present to Mansour later on Tuesday.
The Brotherhood though rejected the plan outright.
"A constitutional decree by a man appointed by putschists... brings the country back to square one," senior Brotherhood official Essam al-Erian said in a Facebook posting.
But the army warned against any disruption of the plans.
A statement read out on state television said neither the armed forces nor the people of Egypt would accept "the stalling or disruption" of this "difficult and complex" period.
The Brotherhood held fresh protests on Tuesday against both Morsi's ouster and the fatal shooting of at least 51 activists outside the Cairo headquarter of the elite Republican Guard.
"Each province is organising funerals and rallies (Tuesday), and each province will have a central sit-in," Brotherhood spokesperson Gehad El-Haddad told AFP.
At Cairo's Rabaa al-Adawiya mosque, where Morsi supporters have been camping out for nearly two weeks, several thousand demonstrators, worn out by the heat, listened to speakers urging them to remain steadfast in their demands for his reinstatement.
Mansour ordered an independent inquiry into the bloodshed outside the Guard's HQ, which sparked expressions of concern and condemnation from around the world.
The Brotherhood released the names of 42 people killed in the shooting, as the interior ministry and military said two policemen and a soldier were also killed.
Emergency services chief Mohammed Sultan said at least 51 people were killed and 435 wounded.
Emotions ran high as people searched for the names of missing loved ones on a list of the dead in hospital, where dozens of bodies were laid on the bloody floor of a makeshift mortuary.
The army warned it would not allow anyone to threaten national security, urging protesters to stay away from military installations and to end their sit-ins.
International condemnation of Monday's bloodshed poured in, with Germany expressing "shock" at the violence, Turkey calling it an attack on "humanity" and Brotherhood backer Qatar urging "self-restraint" and "unity".
The United States called on the Egyptian army to exercise "maximum restraint", while also condemning "explicit" Brotherhood calls to violence.
The Brotherhood's political arm, the Freedom and Justice Party (FJP), had called for "an uprising by the great people of Egypt against those trying to steal their revolution with tanks" in response to Monday's killings.
In the Suez Canal city of Port Said, gunmen on a motorcycle opened fire on a church early Tuesday, wounding a man, witnesses said.
Morsi's single year of turbulent rule was marked by accusations he failed the 2011 revolution that ousted autocratic president Hosni Mubarak by concentrating power in Islamist hands and letting the economy nosedive.
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@Realist: Why win it again if they have won it once, so US says army should ensure proper transitiion, but the champions of democracy have no comments on throwing morsi out.
If you are popular, just win it again. What is the problem?