The National Democratic Party of Hosni Mubarak, the country's long-serving president, is expected to win most of the seats when official results are announced on Thursday.
"None of the brotherhood's candidates have won any seats in 2010 Shura Council elections, a blatant proof that vote rigging took place," Mohamed Saad el-Katatni, the Brotherhood's parliamentary leader, said.
"Many candidates ran in constituencies which they won in the 2005 lower house parliamentary election."
Human rights activists and independent monitors have criticised Tuesday's election as unfair. Candidates from the Brotherhood - which is officially banned - were not allowed to campaign freely, and monitors documented voters being turned away from polling stations and other irregularities.
One man, a representative of a Muslim Brotherhood candidate, was shot by police as he tried to enter a polling station.
El-Katatni said the Brotherhood's exclusion from the Shura Council has stiffened the group's resolve for political reform.
"In a matter of weeks we will begin gathering signatures across the country and from the streets where the Brotherhood has strong presence," el-Katatni said.
He said the Brotherhood will not necessarily back a possible ElBaradei's bid for the presidency.
Impossible to run
ElBaradei has said that he might run, but constitutional rules make it almost impossible for an independent candidate to get on the ballot.
His petition asks the government to make it easier for independents to run for office, and also for an end to Egypt's nearly 30-year-old emergency laws, which were renewed last month.
The government insists elections are free and fair. It says complaints about Tuesday's vote are being investigated.
There is wide ranging speculation that an aging president Mubarak wants to pass the presidency to his son Gamal, who lacks popular appeal.