CAIRO—A broad cross-section of Egyptian political parties lodged strong objections to attempts by the country's ruling military council to expand its authority over the process of drafting the country's first postrevolutionary constitution.

The complaints came on Wednesday after Deputy Prime Minister Ali al-Selmi asked some 500 politicians from among Egypt's newly emerging political parties to sign a proposed set of constitutional "guidelines" that Egypt's interim military leadership would like to see included in the founding...