Final run-offs to the assembly's upper house will end on February 22 instead of March 12 as previously planned, the ruling military council said in a statement, and the house will hold its first sitting on February 28.
Fifty-nine people were killed in confrontations in late November and December between security forces and protesters demanding the military leave power sooner.
Many Egyptians voiced outrage at video footage of soldiers beating men and women after they had already collapsed on the ground, some dragging a female protester by her black full-body veil, exposing her bra then clubbing and kicking her.
Thousands marched on Cairo's Tahrir Square on December 20 to condemn the military's tactics.
Many believe the army is no longer fit to manage security on the ground and carry out difficult reforms at a time of political and economic crisis.
Others say it is the only institution with the credibility to unite the country and prevent Egypt being dragged further into chaos by the opposing political forces freed by the toppling of president Hosni Mubarak in February.
The November demonstrations had already prompted the military rulers to fix mid-2012 as their deadline for quitting power by handing over to a civilian president.
An earlier end to the multi-stage parliamentary election could take some momentum out of the protests, led by pro-democracy groups and rights activists who suspect the army is secretly maneuvering to maintain its autonomy and its broad business interests after the transition.
An army council member had already flagged the possibility of a shorter election to the upper house, or Shura Council, last month.
He said the judiciary had agreed to the idea of squeezing the Shura election into two stages instead of three, and that a plan to shorten the vote tallying process was being studied.
Voters go to the polls next week for the third and concluding round of the lower house election.
Islamist parties that took a secondary role in the protests against Mubarak, but which benefit from strong grass-roots networks, pushed a liberal bloc into third place in the first two rounds.
The first round of the upper house election will take place on January 29 and 30, with a run-off on February 7, the military council said in the statement. The second stage will be on February 14 and 15 with a run-off on February 22.