Biblawi told Reuters he accepted that it would be difficult to win the unanimous support of Egyptians for his new government.
"Of course we respect the public opinion and we try to comply with the expectation of the people, but there is always a time of choice, there is more than one alternative, you cannot satisfy all of the people," he said.
Biblawi, an economist and former finance minister, was named interim prime minister on Tuesday and ElBaradei, a former UN diplomat, has been named vice president. Bahaa-Eldin, a lawyer and member of parliament, is also a leading liberal politician.
A spokesman for Egypt's Muslim Brotherhood says the group will reject any offer to join an interim government to replace the administration of ousted President Mohammed Morsi
A Brotherhood spokesman dismissed any talk of joining a military-backed administration, and said talk of national reconciliation is "irrelevant." He spoke on condition of anonymity because of concerns for his security.
Egypt's main liberal alliance withdrew a statement that rejected outright a constitutional decree announced by the state's interim president and issued more mildly worded criticism.
The National Salvation Front (NSF) reiterated that it was not consulted on the decree and said the plan included articles it did not agree upon, while other important ones were lacking or needed amendments.
The new statement said the NSF would communicate its views to interim President Adli Mansour. The decree sets the rules for the interim period leading to new parliamentary and presidential elections.
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