CAIRO — Egypt’s new rulers gave new credence to a court case against the ousted president, Mohamed Morsi, and members of the Muslim Brotherhood on Thursday over their escape from prison during the uprising that toppled his predecessor, Hosni Mubarak.

The case was transferred from an appeals court to the State Security prosecutor for further investigation. No charges have yet been filed. Its acceptance by powerful prosecutors follows the arrest of many Muslim Brotherhood members and is a new blow to the group by the military-backed government.

The detentions have been criticized by rights groups and the Obama administration, which spent Thursday walking back remarks made early in the day by a State Department spokeswoman, Jen Psaki, seeming to criticize Mr. Morsi as undemocratic and in so doing seeming to validate the military’s move to oust him.

Reuters reported that Ms. Psaki’s counterpart at Egypt’s Foreign Ministry, Badr Abdelatty, interpreted her remarks as a welcome signal that the United States understood “the political developments that Egypt is witnessing in recent days as embodying the will of the millions of Egyptians who took to the streets starting on June 30 to ask for their legitimate rights and call for early elections.”